When we include the variable of time to our Rate Law then we obtain the Integrated Rate Laws.

Concept #1: First, Second and Zeroth Order Reactions

Example #1: The oxidation of ethane follows a first order mechanism, with a very high rate constant of 32 s** ^{-1}**, to form H

Example #2: Iodine-123 is used to study thyroid gland function. This radioactive isotope breaks down in a first order process with a half-life of 8.50 hours at 800 K. How long will it take for the concentration of iodine-123 to be 74.1% complete?

Practice: At 25** ^{o}**C, 2 NOBr (g) ----> 2 NO (g) + Br

Practice: In a typical chemical reaction, nitrogen trioxide, NO_{3}, reacts to produce nitrogen dioxide, NO_{2}, and oxygen gas, O.

2 NO_{3} (g) 2 NO_{2} (g) + 2 O (g)

A plot of [NO_{3}] vs. time is linear and the slope is equal to 0.183. If the initial concentration of NO_{3} is 0.930 M, how long will it take for the final concentration to reach 0.400 M?

Example #3: Part A: Given the following graph for a second order reaction:

a) Calculate the frequency factor.

Example #4: Part B: Calculate the energy of activation in (J/mol).

Practice: The three plots were done based on a chemical reaction. What is the rate constant of the reaction if it takes 21.2 minutes for the reaction to be 38.0% complete?

Concept #2: Half-life is defined as the time it takes for half of the amount of a substance to decay in a certain amount of time.

Concept #3: For zeroth order reactions the concentration of reactants decreases in a uniform manner over time.

Concept #4: For first order reactions the concentration of reactants decreases in a logarithmic manner.

Concept #5: For second order reactions the largest drop in concentration occurs initially followed by a decreasing loss of reactant.

The following reaction is first order, C2H6 → 2 CH3. If the rate constant is equal to 5.5 x 10–4s–1 at 1000 K, how long will it take for the 0.35 mol of C 2H6 in a 1.00L container to decrease to 0.20 mol in the same container?
a) 65 min
b) 17 min
c) 53 min
d) 4.5 min

A 1st order reaction is 65.5 % complete in 32.5 minutes. Determine the half-life of this reaction.
a. 24.8 min
b. 21.2 min
c. 11.2 min
d. 53.2 min
e. 47.1 min

The second-order decomposition of NO2 has a rate constant of 0.255 M –1s –1. How much NO2 decomposes in 4.00 seconds if the initial concentration of NO 2 (1.00 L volume) is 1.33 M?
A. 0.85 mol
B. 0.48 mol
C. 0.56 mol
D. 0.77 mol
E. 1.8 mol

The rate constant for a first-order reaction is 6.47 x 10 -7 hr -1. How long would it take for the reaction to be 28.75% complete?
A. 2.28 x 105 hours
B. 8.37 x 105 hours
C. 6.09 x 105 hours
D. 5.24 x 105 hours
E. 1.93 x 105 hours

The following reaction is first order, C2H6 → 2 CH3. If the rate constant is equal to 5.5 x 10–4 s–1 at 1000 K, how long will it take for 0.35 mol C 2H6 in a 1.00 L conainer to decrease to 0.20 mol in the same container?
A) 65 min
B) 17 min
C) 53 min
D) 4.5 min

For the first-order reaction, the initial concentration of reactant A is 0.882 M. What would be concentration be after 8 half-lives?
a. 0.110 M
b. 0.353 M
c. 0.00345 M
d. 0.00143 M
e. 0.00200 M

A reaction is found to be a second order process with k = 0.215 M -1 hr -1. If the initial concentration is 0.662 M, what would the concentration be after 3.65 days?
A. 0.436 M
B. 0.230 M
C. 0.0492 M
D. 0.203 M
E. 0.03669 M

Which function of [X], plotted against time, will give a straight line for a second order reaction?
(A) [X]
(B) [X]2
(C) ln[X]
(D) 1/[X]

Iodine is absorbed by the thyroid. Iodine-131 is radioactive, emitting both gamma rays and beta particles (electrons), so it can be used diagnostically image the thyroid and therapeutically for the treatment of hyperthyroidism. The radioactive decay of iodine-131 follows first-order kinetics with a half-life of 8.02 days.
a. What is the rate constant for the decay of iodine-131?
b. Assuming an initial dose of 1.0 x 10 -6 g of iodine-131 absorbed by the thyroid, how much would be left after two weeks?

A first order reaction has consumed 66% of the reactants in 8 minutes at 25° C. What is the rate constant?
A) 0.0023 s‐1
B) 0.139 s‐1
C) 8.87 s‐1
D) 3.32 s‐1
E) none of the above

What data should be plotted to show that experimental concetration data fits a first order reaction?
A. 1/[reactant] vs. time
B. [reactant] vs. time
C. In[reactant] vs. time
D. In(k) vs. Ea
E. In(k) vs. 1/T

The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.67 M. What is the rate constant for this reaction?
A. 9.7 x 10-2M-1s-1
B. 4.5 x 10-2M-1s-1
C. 3.8 x 10-2M-1s-1
D. 2.2 x 10-2M-1s-1
E. 1.0 x 10-2M-1s-1

The first-order decay of radon has a half-life of 3.823 days. How many grams of radon remain after 7.22 days if the sample initially weighs 250.0 grams?
A. 183 g
B. 76.3 g
C. 67.5 g
D. 54.8 g
E. 4.21 g

Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon-14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 5.0% of the C-14 found in living organisms. How old is the bone?
A) 1.3 x 104 years
B) 1.0 x 105 years
C) The initial concentration is needed to answer the question.
D) 2.9 x 102 years
E) 2.5 x 104 years

Carbon-14, which is present in all living tissue radioactively decays via a first-order process. A one-gram sample of wood taken from a living tree gives a rate for carbon-14 decay of 13.6 counts per minute. If the half-life for carbon-14 is 5720 years, how old is a wood sample that gives a rate for carbon-14 decay of 11.9 counts per minute?
A. 5.3 x 102 yr
B. 7.6 x 102 yr
C. 1.1 x 103 yr
D. 9.5 x 103 yr

The rate constant for the second order reaction: 2NOBr (g) → 2NO (g) + Br2 (g) is 0.80 M -1 s -1 at 10 °C. Starting with a concentration of 0.086 M, calculate the concentration of NOBr after 22 s.

Olanzapine is an orally-administered antipsychotic drug used to treat schizophrenia and bipolar disorder. Like most drugs (95%), Olanzapine is eliminated by first-order kinetics. The half-life for Olanzapine elimination is 36 hours.
A. Calculate the rate constant for elimination of Olanzapine. (Be sure to include units)
B. The optimal therapeutic range for Olanzapine is 20 to 40 ng/mL. Concentrations of 80 ng/mL are considered to be the upper-limit to avoid adverse side effects.
How long would it take for the concentrations of Olanzapine to drop from 80 ng/mL to 10 ng/mL?
C. By mistake, a patient was given a dose of olanzapine that resulted in a blood serum concentration of 350 ng/mL instead of the desired 35 ng/mL. Calculate how long will it take for the concentration of Olanzapine to drop from 350 ng/mL to 80 ng/mL, the fringe of the "safe zone"?
* Note estimating the amount of time based of half-life is not good enough. Calculate the time required.

The thermal decomposition of N2O5 obeys first-order kinetics. At 45 °C, a plot of ln[N2O5] vs time gives a slope of -6.18 x 10-4 min-1. What is the half-life of the reaction?

At a particular temperature, N2O5 decomposes according to a first-order rate law with a half-life of 3.0 s. If the initial concentration of N2O5 is 1.0 x 1016 molecules/mL, what will be the concentration in molecules/mL after 10.0 sec?
a) 9.9 x 1014
b) 1.8 x 1012
c) 7.3 x 109
d) 6.3 x 103
e) 9.4 x 102

Consider the first order reaction
A → products
where 25% of A disappears in 24 seconds. What is the half life of this reaction?
1. t1/2 = 48s
2. t1/2 = 12s
3. t1/2 = 58s
4. t1/2 = 36s
5. t1/2 = 25s
6. t1/2 = 40s

What is the half life in sec for a first order reaction with k = 2.74 × 10 - 2 s −1?
A. 17.4
B. 20.6
C. 25.3
D. 27.7
E. 29.8

Given the characteristics of a zeroth order reaction having only one reactant,
a) the rate of the reaction is independent to the concentration of the reactant.
b) the rate of the reaction is proportional to the inverse of the concentration of the reactant.
c) the rate of the reaction is proportional to the square of the concentration of the reactant.
d) the rate of the reaction is proportional to the natural logarithm of the concentration of the reactant.
e) the rate of the reaction is directly proportional to the concentration of the reactant.

The second-order reaction, 2 NO2Br (g) → 2 NO2 (g) + Br2 (g), has a half-life of 15.12 mins at 500 K. How long (in hours) will it take for the concentration of NO2Br to fall to 32% of its initial value?

For the first order reaction, 2N 2O (g) → 2 N2 (g) + O2 (g), what is the concentration of N2O after 4 half-lives if 0.75 mol of N 2O is initially placed into a 5.0 L reaction vessel?

The thermal decomposition of acetaldehyde, CH3CHO → CH4 + CO, is a second-order reaction. The following data were obtained at 518°C.
Time, s Pressure CH3CHO, mmHg
0 364
42 330
105 290
720 132
Calculate the rate constant for the decomposition of acetaldehyde from the above data.
A. 2.2 x 10-3/s
B. 0.70 mmHg/s
C. 2.2 x 10-3/mmHg•s
D. 6.7 x 10-6/mmHg•s
E. 5.2 x 10-5/mmHg•s

Which of the following would increase the rate of a zero-order overall reaction:
I. Increase the temperature
II. Increase the concentration
III. Add a catalyst
A. Only I
B. Only II
C. Only III
D. Both I and III
E. All three

Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has 25% of the carbon-14 remaining, then how old is it?
A) 11440 years
B) 2375 years
C) 4750 years
D) 4290 years
E) 1430 years

What is the rate constant of a first-order process that has a half-life of 3.50 min?
A. 0.693 s -1
B. 1.65 × 10 -2 s -1
C. 1.98 s -1
D. 0.198 s -1
E. 3.30 ×10 -3 s -1

Which of the following would increase the rate of a zero-order overall reaction:
I. Increase the temperature
II. Increase the concentration
III. Add a catalyst
A. Only I
B. Only II
C. Only III
D. Both I and III
E. All three

The half-life for a first order reaction is 50 sec when [A] o = 0.84 mol L−1. The time needed for the concentration of A to decrease to one-fourth of its original concentration is:
a) 100 sec
b) 150 sec
c) 75 sec
d) 200 sec
e) 50 sec

The second-order decomposition of NO2 has a rate constant of 0.255 M –1s –1. How much NO2 decomposes in 4.00 seconds if the initial concentration of NO2 (1.00 L volume) is 1.33 M?
A. 0.85 mol
B. 0.48 mol
C. 0.56 mol
D. 0.77 mol
E. 1.8 mol

The half-life for the first order decomposition of C 4H8 is 72.3 s, how long will it take for the partial pressure of C4H8 to decrease from 6.2 atmospheres to 1.8 atmospheres?
a) 135 s
b) 133 s
c) 129 s
d) 127 s
e) 138 s

The decomposition of N2O to give N2 and O2 is second order with a rate constant of 0.051 moles−1•L•s−1. If the initial N2O concentration is 0.58 moles/L, how long will it take for the concentration to drop to one half of its initial value?
a) 33.8 s
b) 86.7 s
c) 13.5 s
d) 26.1 s
e) 29.6 s

For a first order reaction with a rate constant of 5.6x10 −3 s−1, how long will it take for the reactant concentration to fall to one fifth of its initial value?
a) 176 s
b) 428 s
c) 617 s
d) 287 s
e) 592 s

The reaction
2SO3(g) → 2SO2(g) + O2(g)
is second order. If the concentration of SO3 decreases from 0.0360 moles/L to 0.0075 moles/L in 863 s, what is the rate constant for the reaction?
a) 0.476 moles-1 L s−1
b) 0.0987 moles-1 L s−1
c) 5.23 moles-1 L s−1
d) 0.376 moles-1 L s−1
e) 0.122 moles-1 L s−1

The rate constant for the first-order decomposition of N2O is 3.40 s-1. What is the half-life of the decomposition?
A) 0.491 s
B) 0.204 s
C) 0.236 s
D) 0.424 s
E) 0.294 s

The reaction
N2O3(g) → NO2(g) + NO(g)
is first order with a rate constant k = 0.0914 s −1. If a container is filled with N2O3 to a partial pressure of 0.87 atmospheres, how long will it take for the N2O3 partial pressure to fall to 0.63 atmospheres?
a) 87 s
b) 3.5 s
c) 21.6 s
d) 6.8 s
e) 76 s

The half-life for the first order conversion of cyclobutane to ethylene,
C4H8(g) → 2C2H4(g)
is 22.7 s at a particular temperature. How many seconds are needed for the partial pressure of cyclobutane to decrease from 100 mmHg to 10 mmHg?
(A) 52.0 s
(B) 75.4 s
(C) 90.0 s
(D) 227 s

The concentration of an anti-viral drug in a patient’s blood following intravenous drug administration was 6.0 x 10–6 M. After 90 minutes, the concentration of the drug had decreased in a first-order fashion to 1.7 x 10–6 M. If the drug must be re-administered when the concentration in the blood reaches 2.0 x 10–7 M, how long (approximately) after the initial injection will the patient next require the drug?

At 25oC, the rate constant for the first-order decomposition of a solution is k = 6.48 x 10-3 min-1. If the initial concentration of solution is 0.0854 M, what concentration will remain after 185.0 minutes at 25oC?
A. 2.832 M
B. 0.0258 M
C. 0.161 M
D. 1.57 x 10-2 M
E. 2.12 x 10-1 M

Given the following diagrams at t = 0 and t = 30, what is the half-life of the reaction if it follows first-order kinetics?

After four half-life periods for a first-order reaction, what fraction of reactant remains?

A friend studies a first-order reaction and obtains the following three graphs for experiments done at two different temperatures.
Which two graphs represent experiments done with the same starting concentration but at different temperatures?

A first-order reaction AB has the rate constant k = 3.3×10−3 s-1 .If the initial concentration of A is 2.6×10−2 M, what is the rate of the reaction at t = 660 s ?

Anthropologists can estimate the age of a bone or other sample of organic matter by its carbon-14 content. The carbon-14 in a living organism is constant until the organism dies, after which carbon-14 decays with first-order kinetics and a half-life of 5730 years. Suppose a bone from an ancient human contains 15.5 % of the C-14 found in living organisms.How old is the bone?

Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then decays with first-order kinetics and a half-life of 4.5 billion years. A rock is found to contain 83.3% of the amount of uranium-238 that it contained when it was formed. (The amount that the rock contained when it was formed can be deduced from the presence of the decay products of U-238.)How old is the rock?

The following is a quote from an article in the August 18, 1998, issue of The New York Times about the breakdown of cellulose and starch: "A drop of 18 degrees Fahrenheit [from 77 oF to 59 oF] lowers the reaction rate six times; a 36-degree drop [from 77 oF to 41 oF] produces a fortyfold decrease in the rate."Assuming the value of Ea calculated from the 36-degree drop and assuming that the rate of breakdown is first order with a half-life at 25 oC of 2.7 years, calculate the half-life for breakdown at a temperature of -15 oC.

The half-life for radioactive decay (a first-order process) of plutonium-239 is 24,000 years.How many years would it take for one mole of this radioactive material to decay so that just one atom remains?

Dinitrogen pentoxide (N2 O5) decomposes in chloroform as a solvent to yield NO2 and O2. The decomposition is first order with a rate constant at 45 oC of 1.0 10 - 5 - 1.Calculate the partial pressure of O2 produced from 1.51 L of 0.601 M
N2 O5 solution at 45 oC over a period of 20.1 h if the gas is collected in a 11.6-L container. (Assume that the products do not dissolve in chloroform.)

The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide was found to be first order with a rate constant of 0.128/s at 150 K.What is the half-life of the desorption reaction?

The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide was found to be first order with a rate constant of 0.128/s at 150 K.If the surface is initially completely covered with n-butane at 150 K, how long will it take for 25% of the molecules to desorb (leave the surface)?

Americium-241 is used in smoke detectors. It has a
first order rate constant for radioactive decay of k = 1.6 10-3-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1.Which one decays at a faster rate?

Americium-241 is used in smoke detectors. It has a
first order rate constant for radioactive decay of k = 1.6 10-3-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1.How much of a 1.00 mg
sample of americium remains after 3 half-lives?

Americium-241 is used in smoke detectors. It has a
first order rate constant for radioactive decay of k = 1.6 10-3-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1.What is the half-life of americium-241?

Americium-241 is used in smoke detectors. It has a
first order rate constant for radioactive decay of k = 1.6 10-3-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1.How much of a 1.00 mg sample of iodine remains after 3 half-lives?

Americium-241 is used in smoke detectors. It has a
first order rate constant for radioactive decay of k = 1.6 10-3-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1.How much of a 1.00 mg sample of americium remains after 4 days?

Americium-241 is used in smoke detectors. It has a
first order rate constant for radioactive decay of k = 1.6 10-3-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1.How much of a 1.00 mg sample of iodine remains after 4 days?

A first-order reaction (A B 25) has a half-life of A minutes.
If the initial concentration of A is 0.600
B, what is the concentration of A after
50 minutes? (Do not use a calculator to solve this problem.)

The images shown here depict the first-order reaction A B A at
various times during the reaction process. The black circles represent reactant A and the
red circles represent product A.
What is the half-life of the reaction?

The decomposition of sulfuryl chloride (SO2 Cl2 ) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 10-2-1.If we begin with an initial SO2 Cl2 pressure of 460 torr , what is the partial
pressure of this substance after 66 s ?

If a solution containing 26.0
g of a substance reacts by first-order kinetics, how many grams remain after three half-lives?

Does the half-life of a second-order reaction increase, decrease, or remain the same as the reaction
proceeds?

Does the half-life of a zero-order reaction depend on the initial concentration of the
reactant?

Explain the difference between the rate law for a reaction and the integrated rate law for a reaction.
What relationship does each kind of rate law express?

Half-life equation for first-order reactions: t 1/2=0.693/k where t1/2 is the half-life in seconds , and k is the rate constant in inverse seconds.
What is the half-life of a first-order reaction with a rate constant of 8.80 x 10 -4 s-1?

For a second-order reaction, a straight line is obtained from a plot ofa) [A] vs. t b) ln(1/t) vs. [A] c) ln(t) vs. [A] d) 1/[A] vs. t e) ln[A] vs. t

What data should be plotted to show that experimental concentration data fits a second-order reaction?
A. [reactant] vs. time
B. In[reactant] vs. time
C. In(k) vs. Ea
D. In(k) vs. 1/T
E. 1/[reactant] vs. time

The rate of conversion from cyclopropane to propene in the gas phase at constant temperature is a first order reaction. From the information in the graph, which statement about the half-life of the conversion reaction is true?(A) It is approximately equal to 150 s.(B) It is approximately equal to 270 s.(C) It is approximately equal to 420 s.(D) It cannot be determined.

The decomposition of dinitrogen pentoxide, N2O5, to NO2 and O2 is a first-order reaction. At 60°C, the rate constant is 2.8 × 10-3 min-1. If a rigid vessel initially contains only N 2O5 at a pressure of 125 kPa, how long will it take for the total pressure to reach 176 kPa?
a. 113 min
b. 129 min
c. 42 min
d. 182 min
e. 62 min
f. 83 min

Radioactive plutonium-239 (t1/2 = 2.44 x 105 yr) is used in nuclear reactors and atomic bombs. If there are 4.00 x 102 g of isotope in a small atomic bomb, how long will it take for the substance to decay to 1.00 x 102 g? Hint: Radioactive decays follow first-order kinetics.

Which of the following statements is FALSE?a) The average rate of a reaction decreases during a reaction.b) It is not possible to determine the rate of a reaction from its balanced equation.c) The rate of zero order reactions are not dependent on concentration.d) The half life of a first order reaction is dependent on the initial concentration of reactant.

The first-order decomposition of N2O at 1000 K has a rate constant of 0.76 s‒1. If the initial concentration of N2O is 10.9 M, what is the concentration of N 2O after 9.6 s? A) 1.0 × 10‒3 MB) 8.7 × 10‒3 MC) 1.4 × 10‒3 MD) 3.6 × 10‒3 ME) 7.4 × 10‒3 M

Indicate whether each statement refers to zero order, first order, or second order.
a. The half-life of the reaction gets shorter as the initial concentration is increased.
b. A plot of the natural log of the concentration of the reactant versus time yields a straight line.
c. The half-life of the reaction gets longer as the initial concentration is increased.

What are the units for each of the following if the concentrations are expressed in moles per liter and the time in seconds? c. rate constant for a first‑order rate law

Chlorine is commonly used to disinfect drinking water, and inactivation of pathogens by chlorine follows first-order kinetics. The following data are for E. coli inactivation:Determine the first-order inactivation constant, k. [ Hint: % inactivation = 100 x (1 – [A] t/[A]0).]

The gas-phase decomposition of SO2Cl2, SO2Cl2(g) → SO2 (g) + Cl2 (g), is first order in SO2Cl2. At 600 K the half-life for this process is 2.3 x 105 s.What is the rate constant at this temperature?

Chlorine is commonly used to disinfect drinking water, and inactivation of pathogens by chlorine follows first-order kinetics. The following data are for E. coli inactivation:How much contact time is required for 95% inactivation?

The gas-phase decomposition of SO2Cl2, SO2Cl2(g) → SO2 (g) + Cl2 (g), is first order in SO2Cl2. At 600 K the half-life for this process is 2.3 x 105 s.At 320 oC the rate constant is 2.2 x 10 - 5 s- 1. What is the half-life at this temperature?

Molecular iodine, I2(g), dissociates into iodine atoms at 625 K with a first-order rate constant of 0.271 s-1 .What is the half-life for this reaction?

A biochemist studying the breakdown of the insecticide DDT finds that it decomposes by a first-order reaction with ahalf-life of 12 yr. How long does it take DDT in a soil sample to decrease from 275 ppbm to 10. ppbm (parts per billion by mass)?

Molecular iodine, I2(g), dissociates into iodine atoms at 625 K with a first-order rate constant of 0.271 s-1 .If you start with 0.055 M of I2 at this temperature, how much will remain after 2.56 s assuming that the iodine atoms do not recombine to form I2?

Insulin is a polypeptide hormone that is released into the blood from the pancreas and stimulates fat and muscle to take up glucose; the insulin is used up in a first-order process. In a certain patient, this process has a half-life of 3.5 min. To maintain an adequate blood concentration of insulin, it must be replenished in a time interval equal to 1/k. How long is the time interval for this patient?

The first-order rate constant for the decomposition of N2O5,2N2O5(g) → 4NO2(g) + O2(g)at 70oC is 6.82 x 10 - 3 s - 1. Suppose we start with 2.60×10−2 mol of N2O5(g) in a volume of 2.1 L .How many moles of N2O5 will remain after 6.0 min ?

The first-order rate constant for the decomposition of N2O5,2N2O5(g) → 4NO2(g) + O2(g)at 70oC is 6.82 x 10 - 3 s - 1. Suppose we start with 2.60×10−2 mol of N2O5(g) in a volume of 2.1 L .How many minutes will it take for the quantity of N2O5 to drop to 1.8×10−2 mol ?

The first-order rate constant for the decomposition of N2O5,2N2O5(g) → 4NO2(g) + O2(g)at 70oC is 6.82 x 10 - 3 s - 1. Suppose we start with 2.60×10−2 mol of N2O5(g) in a volume of 2.1 L .What is the half-life of N2O5 at 70oC?

The reaction SO2Cl2(g) → SO2 (g) + Cl2 (g) is first order in SO2 Cl2.Using the following kinetic data, determine the magnitude of the first-order rate constant: Time (s) Pressure SO2Cl2 (atm) 01.00025000.94750000.89575000.848100000.803

From the following data for the first-order gas-phase isomerization of CH3 NC at 215 oC, calculate the first-order rate constant and half-life for the reaction:Time (s) Pressure CH3NC (torr)050220003355000180800095.51200041.71500022.4Calculate the first-order rate constant.

The decomposition of SO2Cl2 is first order in SO2Cl2 and has a rate constant of 1.44×10−4 s-1 at a certain temperature. What is the half-life for this reaction?

From the following data for the first-order gas-phase isomerization of CH3 NC at 215 oC, calculate the first-order rate constant and half-life for the reaction:Time (s) Pressure CH3NC (torr)050220003355000180800095.51200041.71500022.4Calculate the half-life.

The decomposition of SO2Cl2 is first order in SO2Cl2 and has a rate constant of 1.44×10−4 s-1 at a certain temperature. How long will it take for the concentration of SO2Cl2 to decrease to 25% of its initial concentration?

A friend studies a first-order reaction and obtains the following three graphs for experiments done at two different temperatures.Which two graphs represent experiments done at the same temperature? What accounts for the difference in these two graphs? In what way are they the same?

The decomposition of SO2Cl2 is first order in SO2Cl2 and has a rate constant of 1.44×10−4 s-1 at a certain temperature. If the initial concentration of SO2Cl2 is 1.00 M, how long will it take for the concentration to decrease to 0.78 M ?

The decomposition of SO2Cl2 is first order in SO2Cl2 and has a rate constant of 1.44×10−4 s-1 at a certain temperature. If the initial concentration of SO2Cl2 is 0.175 M, what is the concentration of SO2Cl2 after 210 s?

The decomposition of SO2Cl2 is first order in SO2Cl2 and has a rate constant of 1.44×10−4 s-1 at a certain temperature. If the initial concentration of SO2 Cl2 is 0.175 M, what is the concentration of SO2Cl2 after 510 s?

Nitrification is a biological process for removing NH 3 from wastewater as NH4+:NH4+ + 2 O 2 ⟶ NO3− + 2 H+ + H2OThe first-order rate constant is given ask1 = 0.47e0.095(T − 15˚C)where k1 is in day −1 and T is in ˚C. If the initial concentration of NH 3 is 3.0 mol/m3, how long will it take to reduce the concentration to 0.35 mol/m3 in the spring (T = 20˚C)?

The rate of the reactionO (g) + NO2 (g) → NO (g) + O2 (g)was studied at a certain temperature.a. In one experiment, NO2 was in large excess, at a concentration of 1.0 x 10 13 molecules/cm3 with the following data collected:What is the order of the reaction with respect to oxygen atoms?b. The reaction is known to be first order with respect to NO 2. Determine the overall rate law and the value of the rate constant.

Nitrification is a biological process for removing NH 3 from wastewater as NH4+:NH4+ + 2 O 2 ⟶ NO3− + 2 H+ + H2OThe first-order rate constant is given ask1 = 0.47e0.095(T − 15˚C)where k1 is in day −1 and T is in ˚C. If the initial concentration of NH 3 is 3.0 mol/m3, how long will it take to reduce the concentration to 0.35 mol/m3 in the winter (T = 10˚C)?

Nitrification is a biological process for removing NH 3 from wastewater as NH4+:NH4+ + 2 O 2 ⟶ NO3− + 2 H+ + H2OThe first-order rate constant is given ask1 = 0.47e0.095(T − 15˚C)where k1 is in day −1 and T is in ˚C. (a) If the initial concentration of NH3 is 3.0 mol/m3, how long will it take to reduce the concentration to 0.35 mol/m3 in the spring (T = 20°C)?Using your answer to part (a), what is the rate of O 2 consumption?

A first-order reaction is 75.0% complete in 320. s.b. How long does it take for 90.0% completion?

At 25°C the decomposition of N2O5 (g) into NO2 (g) and O2(g) follows first-order kinetics with k = 3.4 10-5 s-1. How long will it take for a sample originally containing 2.0 atm of N2O5 to reach a partial pressure of 380 torr?

A certain first-order reaction has a rate constant of 2.55×10−2 s-1 at 21 oC. What is the value of k at 61 oC if Ea exttip{E_a}{E_1}= 81.0 kJ/mol ?

Another first-order reaction also has a
rate constant of 2.55×10−2 s-1 at 21 oC. What is the value of k at 61 oC if Ea exttip{E_a}{E_2}= 118 kJ/mol ?

At 25oC, the decomposition of dinitrogen pentoxide, N2O5(g), into NO2(g) and O2(g) follows first-order kinetics with k = 3.410-5 s-1. A sample of N2O5 with an initial pressure of 760 torr decomposes at 25oC until its partial pressure is 650 torr. How much time (in seconds) has elapsed?

The half-life for the radioactive decay of C-14 is 5730 years.
a. How long will it take for 30% of the C-14 atoms in a sample of C-14 to decay?
Express your answer using two significant figures.
b. If a sample of C-14 initially contains 1.9mmol of C-14, how many millimoles will be left after 2255 years?
Express your answer using two significant figures.

Many drugs decompose in blood by a first-order process.(a) Two tablets of aspirin supply 0.60 g of the active compound. After 30 min, this compound reaches a maximum concentration of 2 mg/100 mL of blood. If the half-life for its breakdown is 90 min, what is its concentration (in mg/100 mL) 2.5 h after it reaches its maximum concentration?

Many drugs decompose in blood by a first-order process.(b) For the decomposition of an antibiotic in a person with a normal temperature (98.6°F), k = 3.1 x 10-5 s-1; for a person with a fever (temperature of 101.9°F), k = 3.9 x 10-5 s-1. If the person with the fever must take another pill when 2/3 of the first pill has decomposed, how many hours should she wait to take a second pill? A third pill? (Assume that the pill is effective immediately.)

Many drugs decompose in blood by a first-order process.(c) Calculate Ea for decomposition of the antibiotic in part (b).

The growth of Pseudomonas bacteria is modeled as a first-order process with k = 0.035 min −1 at 37˚C. The initial Pseudomonas population density is 1.0 x 10 3 cells/L. What is the population density after 2 h?

Dinitrogen pentoxide decomposes in the gas phase to form nitrogen dioxide and oxygen gas. The reaction is first order in dinitrogen pentoxide and has a half-life of 2.81 h at 25 oC. If a 1.6-L reaction vessel initially contains 750 torr of N2O5 at 25 oC, what partial pressure of O2 will be present in the vessel after 220 minutes?

Cyclopropane (C3H6) reacts to form propene (C3H6) in the gas phase. The reaction is first order in cyclopropane and has a rate constant of 5.87 x 10–4 at 485 oC. If a 2.5 L reaction vessel initially contains 723 torr of cyclopropane at 485 oC, how long in minutes will it take for the partial pressure of cyclopropane to drop to below 103 torr?

A certain first-order reaction is 45.0% complete in 65 s. What are the values of the rate constant and the half-life for this process?

A first-order reaction is 75.0% complete in 320. s.a. What are the first and second half-lives for this reaction?

The hydrolysis of sucrose (C12H22O11) into glucose and fructose in acidic water has a rate constant of 1.8 x 10–4 s–1 at 25 oC. Assuming the reaction is first order in sucrose, determine the mass of sucrose that is hydrolyzed when 2.60 L of a 0.160 M sucrose solution is allowed to react for 200 min.

The growth of Pseudomonas bacteria is modeled as a first-order process with k = 0.035 min −1 at 37˚C. The initial Pseudomonas population density is 1.0 x 10 3 cells/L. What is the time required for the population to go from 1.0 x 10 3 to 2.0 x 10 3 cells/L?

DDT (molar mass = 354.49 g/mol) was a widely used insecticide that was banned from use in the United States in 1973. This ban was brought about due to the persistence of DDT in many different ecosystems, leading to high accumulations of the substance in many birds of prey. The insecticide was shown to cause a thinning of egg shells, pushing many birds toward extinction. If a 20-L drum of DDT was spilled into a pond, resulting in a DDT concentration of 8.75 x 10-5 M, how long would it take for the levels of DDT to reach a concentration of 1.41 x 10-7 M (a level that is generally assumed safe in mammals)? Assume the decomposition of DDT is a first-order process with a half-life of 56.0 days.

The reaction 2 H2O2(aq) → H2O(l) + O2(g) is first order in H2O2 and under certain conditions has a rate constant of 0.00752 s-1 at 20.0 oC. A reaction vessel initially contains 150.0 mL of 30.0% H2O2 by mass solution (the density of the solution is 1.11 g/mL). The gaseous oxygen is collected over water at 20.0 oC as it forms.What volume of O2 will form in 64.6 seconds at a barometric pressure of 750.1 mmHg. (The vapor pressure of water at this temperature is 17.5 mmHg)

What is the half-life for the first-order decay of phosphorus-32? (1532 P ⟶ 16 32S + e−) The rate constant for the decay is 4.85 × 10−2 day−1 .

What is the half-life for the first-order decay of carbon-14? (614C⟶ 714 N + e− ) The rate constant for the decay is 1.21 × 10−4 year−1 .

A certain substance X decomposes. It is found that 50% of X remains after 100 minutes. How much X remains after 200 minutes if the reaction order with respect to X is first order?

Ethyl chloride vapor decomposes by the first-order reaction C2H5Cl → C2H4 + HCl. The activation energy is 249 kJ/mol and the frequency factor is 1.61014 s-1.Find the fraction of the ethyl chloride that decomposes in 16 minutes at this 720K.

The specific rate constant for the first-order decomposition of N2O5 (g) to NO2(g) and O2(g) is 7.48 x 10-3 s-1 at a given temperature. Find the length of time required for the total pressure in a system containing N2O5 at an initial pressure of 0.110 atm to rise to 0.155 atm.

The specific rate constant for the first-order decomposition of N2O5 (g) to NO2(g) and O2(g) is 7.48 x 10-3 s-1 at a given temperature. Find the length of time required for the total pressure in a system containing N2O5 at an initial pressure of 0.110 atm to rise to 0.220 atm .

The specific rate constant for the first-order decomposition of N2O5 (g) to NO2(g) and O2(g) is 7.48 x 10-3 s-1 at a given temperature. Find the total pressure after 120 s of reaction.

The accompanying graph shows the concentration of a reactant as a function of time for two different reactions. One of the reactions is first order and the other is second order.Which of the two reactions is first order?

The first-order rate constant for the reaction A (green) → B (yellow) is 0.063 min-1. The scenes below represent the reaction mixture at two different times:What is the time at which the second scene occurs?

The molecular scenes below represent the first-order reaction in which cyclopropane (red) is converted to propene (green):Determine (a) the half-life

The molecular scenes below represent the first-order reaction in which cyclopropane (red) is converted to propene (green):Determine (b) the rate constant.

In a first-order decomposition reaction, 50.0% of a compound decomposes in 10.5 min. (a) What is the rate constant of the reaction?

In a first-order decomposition reaction, 50.0% of a compound decomposes in 10.5 min.(b) How long does it take for 75.0% of the compound to decompose?

These images represent the first order reaction A initially and at some later time. The rate law for the reaction is Rate = 0.010 s-1 [A].How much time has passed between the two images?

The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide was found to be first order with a rate constant of 0.128/s at 150 K.If the surface is initially completely covered, what fraction will remain covered after 14 s?

The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide was found to be first order with a rate constant of 0.128/s at 150 K.If the surface is initially completely covered with n-butane at 150 K, how long will it take for 50% to desorb (leave the surface)?

The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide was found to be first order with a rate constant of 0.128/s at 150 K.If the surface is initially completely covered, what fraction will remain covered after 22 s?

The first-order integrated rate law for a reaction A is derived from the rate law using calculus as follows:large{egin{array}{l} { m{Rate}} = k[{ m{A}}]quad quad ({ m{first - order;rate;law)}} { m{Rate}} = - frac{{d[{ m{A}}]}}{{dt}} frac{{d[{ m{A}}]}}{{dt}} = - k[{ m{A}}] end{array}}The above equation is a first-order, separable differential equation that can be solved by separating the variables and integrating:large{egin{array}{c} frac{{d[{ m{A}}]}}{{[{ m{A}}]}} = - k,dt int_{[{ m{A}}]_0 }^{[{ m{A}}]} {frac{{d[{ m{A}}]}}{{[{ m{A}}]}}} = - int_0^t { k,dt} end{array}}In the above integral, [A]0 is the initial concentration of A. We then evaluate the integral:Use a procedure similar to the one above to derive an integrated rate law for a reaction A →products which is one-half order in the concentration of A (that is, Rate = k[A]1/2).

The first-order integrated rate law for a reaction A is derived from the rate law using calculus as follows:The above equation is a first-order, separable differential equation that can be solved by separating the variables and integrating:In the above integral, [A]0 is the initial concentration of A. We then evaluate the integral:Use a procedure similar to the one above to derive an integrated rate law for a reaction A →products which is one-half order in the concentration of A (that is, Rate = k[A]1/2). Use the result to derive an expression for the half-life of a one-half-order reaction.

The rate of decomposition of N2O3(g) to NO2(g) and NO(g) is followed by measuring [NO2] at different times. The following data are obtained.[NO2] (mol/L) 0 0.193 0.316 0.427 0.784t (s) 0 884 1610 2460 50,000 The reaction follows a first-order rate law. Calculate the rate constant. Assume that after 50,000 s all the N2O3(g) had decomposed.

You may want to reference (Pages 582 - 587) Section 14.4 while completing this problem.For the generic reaction A → B what quantity, when graphed versus time, will yield a straight line for a first-order reaction?

You may want to reference (Pages 582 - 587) Section 14.4 while completing this problem.For the generic reaction A → B what quantity, when graphed versus time, will yield a straight line for a first-order reaction? How can you calculate the rate constant for a first-order reaction from the graph you made?

You may want to reference (Pages 568 - 621) Chapter 14 while completing this problem.The reaction H2O2(aq) → H2O(l) + 1/2 O2(g) is first order. At 300 K the rate constant equals 7.0 x 10–4 s–1. Calculate the half-life at this temperature.

Cyclopropane rearranges to form propene in the gas phase.The reaction is first order in cyclopropane and has a measured rate constant of 3.36 x 10-5 s-1 at 720 K. If the initial cyclopropane concentration is 0.0505 M, what is the cyclopropane concentration after 251 minutes?

A first-order reaction has a half-life of 22.6 s . How long does it take for the concentration of the reactant in the reaction to fall to one-fourth of its initial value?

The mathematics of the first-order rate law can be applied to any situation in which a quantity decreases by a constant fraction per unit of time (or unit of any other variable).As light moves through a solution, its intensity decreases per unit distance traveled in the solution. Show that

The mathematics of the first-order rate law can be applied to any situation in which a quantity decreases by a constant fraction per unit of time (or unit of any other variable).The value of your savings declines under conditions of constant inflation. Show that

Acetone is one of the most important solvents in organic chemistry, used to dissolve everything from fats and waxes to airplane glue and nail polish. At high temperatures, it decomposes in a first-order process to methane and ketene (CH2=C=O). At 600˚C, the rate constant is 8.7 x 10−3 s−1. What is the half-life of the reaction?

Acetone is one of the most important solvents in organic chemistry, used to dissolve everything from fats and waxes to airplane glue and nail polish. At high temperatures, it decomposes in a first-order process to methane and ketene (CH2=C=O). At 600˚C, the rate constant is 8.7 x 10−3 s−1. How long does it take for 40.% of a sample of acetone to decompose?

Acetone is one of the most important solvents in organic chemistry, used to dissolve everything from fats and waxes to airplane glue and nail polish. At high temperatures, it decomposes in a first-order process to methane and ketene (CH2=C=O). At 600˚C, the rate constant is 8.7 x 10−3 s−1. How long does it take for 90.% of a sample of acetone to decompose?

The rate law for the reaction HOCl + NH 3 ⟶ NH2Cl + H2O is rate = k[HOCl][NH3] with k = 5.1 x 106 L/mol•s at 25˚C. The reaction becomes pseudo–first-order in NH 3 by using a large excess of HOCl. How long does it take for 30% of the NH3 to react if the initial concentration of HOCl is 2 x 10–3 M?

The decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 x 10–2 s–1. At what time will the partial pressure of SO2Cl2 decline to one-tenth its initial value?

Consider the following representation of the reaction2NO2 (g) → 2NO (g) + O2 (g).Determine the time for the final representation above if the reaction isa. first orderb. second orderc. zero order

Consider two reaction vessels, one containing A and the other containing B, with equal concentrations at t = 0. If both substances decompose by first-order kinetics, wherekA = 4.50 x 10-4 s-1kB = 3.70 x 10-3 s-1how much time must pass to reach a condition such that [A] = 4.00[B]?

The hydrolysis of the sugar sucrose to the sugars glucose and fructose, C12H22O11 + H2O ⟶ C6H12O6 + C6H12O6 follows a first-order rate equation for the disappearance of sucrose: Rate = k[C12H22O11] (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.)(b) When a solution of sucrose with an initial concentration of 0.150 M reaches equilibrium, the concentration of sucrose is 1.65 × 10−7 M. How long will it take the solution to reach equilibrium at 27 °C in the absence of a catalyst? Because the concentration of sucrose at equilibrium is so low, assume that the reaction is irreversible.

Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for 1 64 of the initial dose to remain in the athlete’s body?

Nitroglycerine is an extremely sensitive explosive. In a series of carefully controlled experiments, samples of the explosive were heated to 160 °C and their first-order decomposition studied. Determine the average rate constants for each experiment using the following data:

For the past 10 years, the unsaturated hydrocarbon 1,3-butadiene (CH2 = CH – CH = CH2 ) has ranked 38th among the top 50 industrial chemicals. It is used primarily for the manufacture of synthetic rubber. An isomer exists also as cyclobutene:The isomerization of cyclobutene to butadiene is first-order and the rate constant has been measured as 2.0 × 10−4 s −1 at 150 °C in a 0.53-L flask. Determine the partial pressure of cyclobutene and its concentration after 30.0 minutes if an isomerization reaction is carried out at 150 °C with an initial pressure of 55 torr.

The half-life of a reaction of compound A to give compounds D and E is 8.50 min when the initial concentration of A is 0.150 mol/L. How long will it take for the concentration to drop to 0.0300 mol/L if the reaction is (a) first order with respect to A or

Both technetium-99 and thallium-201 are used to image heart muscle in patients with suspected heart problems. The half-lives are 6 h and 73 h, respectively. What percent of the radioactivity would remain for each of the isotopes after 2 days (48 h)?

What are the units for each of the following if the concentrations are expressed in moles per liter and the time in seconds? d. rate constant for a second‑order rate law

The decomposition of XY is second order in XY and has a rate constant of 7.02×10−3 M-1 s-1 at a certain temperature. What is the half-life for this reaction at an initial concentration of 0.100 M?

The decomposition of XY is second order in XY and has a rate constant of 7.02×10−3 M-1 s-1 at a certain temperature. How long will it take for the concentration of XY to decrease to 12.5% of its initial concentration when the initial concentration is 0.100 M?

The decomposition of XY is second order in XY and has a rate constant of 7.02×10−3 M-1 s-1 at a certain temperature. If the initial concentration of XY is 0.160 M, how long will it take for the concentration to decrease to 6.40×10−2 M?

The decomposition of XY is second order in XY and has a rate constant of 7.02×10−3 M-1 s-1 at a certain temperature. If the initial concentration of XY is 0.050 M, what is the concentration of XY after 55.0 s?

The decomposition of XY is second order in XY and has a rate constant of 7.02×10−3 M-1 s-1 at a certain temperature. How long will it take for the concentration of XY to decrease to 12.5% of its initial concentration when the initial concentration is 0.200 M?

The decomposition of XY is second order in XY and has a rate constant of 7.02×10−3 M-1 s-1 at a certain temperature. If the initial concentration of XY is 0.050 M, what is the concentration of XY after 600 s?

Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide (NO) to N2 and O2 is second order with a rate constant of 0.0796 M - 1 s- 1 at 737oC and 0.0815 M - 1 s- 1 at 947oC.Calculate the activation energy for the reaction.

Iodine atoms will combine to form I2 in liquid hexane solvent with a rate constant of 1.5 x 1010 L/mol•s. The reaction is second order in I. Since the reaction occurs so quickly, the only way to study the reaction is to create iodine atoms almost instantaneously, usually by photochemical decomposition of I2. Suppose a flash of light creates an initial [I] concentration of 2.00 x 10−2 M. How long will it take for 92% of the newly created iodine atoms to recombine to form I2?

The reaction AB(aq) → A(g) + B(g) is second order in AB and has a rate constant of 0.0201 M-1 s-1 at 25.0 oC. A reaction vessel initially contains 250.0 mL of 0.151 M AB which is allowed to react to form the gaseous product. The product is collected over water at 25.0 oC.How much time is required to produce 201.0 mL of the products at a barometric pressure of 750.1 mmHg. (The vapor pressure of water at this temperature is 23.8 mmHg.)

What is the half-life for the decomposition of NOCl when the concentration of NOCl is 0.15 M? The rate constant for this second-order reaction is 8.0 × 10−8 L/mol/s.

What is the half-life for the decomposition of O3 when the concentration of O3 is 2.35 × 10−6 M? The rate constant for this second-order reaction is 50.4 L/mol/h.

The reaction of compound A to give compounds C and D was found to be second-order in A. The rate constant for the reaction was determined to be 2.42 L/mol/s. If the initial concentration is 0.500 mol/L, what is the value of t1/2?

A certain substance X decomposes. It is found that 50% of X remains after 100 minutes. How much X remains after 200 minutes if the reaction order with respect to X is second order?

The accompanying graph shows the concentration of a reactant as a function of time for two different reactions. One of the reactions is first order and the other is second order.Which of the two reactions is second order?

The reaction X → products is second order in X and has a rate constant of 0.035 M-1s-1. If a reaction mixture is initially 0.55 M in X, what is the concentration of X after 151 seconds?

For a generic second-order reaction A → B, what quantity, when graphed versus time, will yield a straight line?

The first-order integrated rate law for a reaction A → products is derived from the rate law using calculus as follows:large{egin{array}{l} { m{Rate}} = k[{ m{A}}]quad quad ({ m{first - order;rate;law)}} { m{Rate}} = - frac{{d[{ m{A}}]}}{{dt}} frac{{d[{ m{A}}]}}{{dt}} = - k[{ m{A}}] end{arrayThe above equation is a first-order, separable differential equation that can be solved by separating the variables and integrating:large{egin{array}{c} frac{{d[{ m{A}}]}}{{[{ m{A}}]}} = - k,dt int_{[{ m{A}}]_0 }^{[{ m{A}}]} {frac{{d[{ m{A}}]}}{{[{ m{A}}]}}} = - int_0^t { k,dt} end{array}}In the above integral, [A]0 is the initial concentration of A. We then evaluate the integral:Begin
with the second-order differential rate law and derive the second-order integrated rate law.

Experiments show that each of the following redox reactions is second order overall:Reaction 1: NO2(g) + CO(g) ⟶NO(g) + CO2(g)Reaction 2: NO(g) + O3(g) ⟶NO2(g) + O2(g)(c) In each reaction, the initial concentrations of the reactants are equal. For each reaction, what is the ratio of the initial rate to the rate when the reaction is 50% complete?

Experiments show that each of the following redox reactions is second order overall:Reaction 1: NO2(g) + CO(g) ⟶NO(g) + CO2(g)Reaction 2: NO(g) + O3(g) ⟶NO2(g) + O2(g)(d) In reaction 1, the initial [NO2] is twice the initial [CO]. What is the ratio of the initial rate to the rate at 50% completion?

Experiments show that each of the following redox reactions is second order overall:Reaction 1: NO2(g) + CO(g) ⟶NO(g) + CO2(g)Reaction 2: NO(g) + O3(g) ⟶NO2(g) + O2(g)(e) In reaction 2, the initial [NO] is twice the initial [O3]. What is the ratio of the initial rate to the rate at 50% completion?

The decomposition of XY is second order in XY and has a rate constant of 7.02 X 10-3 M-1 x S-1 at a certain temperature.
a. What is the half life for this reaction at an initial concentration of 0.100M?
b. How long will it take for the concentration of XY to decrease to 12.5% of its intial concentration when the initial concentration is 0.100M? When the initial concentration is 0.200M?
c. If the initial concentration of XY is 0.150 M, how long will it take for the concentration to decrease to 0.062 M?
d. If the inital concentration of XY is 0.150 M, what is the concentration of XY after 5.0 X 101 s? After 5.50 X 102 s?

The half-life of a reaction of compound A to give compounds D and E is 8.50 min when the initial concentration of A is 0.150 mol/L. How long will it take for the concentration to drop to 0.0300 mol/L if the reaction is(b) second order with respect to A?

You may want to reference (Pages 593 - 600) Section 14.6 while completing this problem.The reaction 2 NO(g) + Cl2(g) → 2 NOCl(g) was performed and the following data were obtained under conditions of constant [Cl2]:Does the linear plot guarantee that the overall rate law is
second order?

What are the units for each of the following if the concentrations are expressed in moles per liter and the time in seconds? b. rate constant for a zero‑order rate law

The reactionA → B + Cis known to be zero order in A and to have a rate constant of 5.0 x 10 -2 mol/L•s at 25°C. An experiment was run at 25°C where [A]0 = 1.0 x 10 -3 M.b. Calculate the half-life for the reaction.

The reactionA → B + Cis known to be zero order in A and to have a rate constant of 5.0 x 10 -2 mol/L•s at 25°C. An experiment was run at 25°C where [A]0 = 1.0 x 10 -3 M.c. Calculate the concentration of B after 5.0 x 10 -3 s has elapsed assuming [B]0 = 0.

The decomposition of hydrogen iodide on finely divided gold at 150°C is zero order with respect to HI. The rate defined below is constant at 1.20 x 10-4 mol/L•s.b. How long will it take for all of the 0.250 M HI to decompose?

Sucrose (C12H22O11 ), which is commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H12O6. At 23 oC and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose:Time (min) C12H22O11 (M)00.316390.274800.2381400.1902100.146Using the rate constant, calculate the concentration of sucrose at 39 min if the initial sucrose concentration were 0.316 M and the reaction were zero order in sucrose.

Sucrose (C12H22O11 ), which is commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H12O6. At 23 oC and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose:Time (min) C12H22O11 (M)00.316390.274800.2381400.1902100.146Using the rate constant, calculate the concentration of sucrose at 80 min if the initial sucrose concentration were 0.316 M
and the reaction were zero order in sucrose.

Sucrose (C12H22O11 ), which is commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H12O6. At 23 oC and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose:Time (min) C12H22O11 (M)00.316390.274800.2381400.1902100.146Using the rate constant, calculate the concentration of sucrose at 140 min if the initial sucrose concentration were 0.316 M
and the reaction were zero order in sucrose.

Sucrose (C12 H22 O11 ), which is commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6 H12 O6. At 23 oC and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose:Time (min) C12H22O11 (M)00.316390.274800.2381400.1902100.146(b) What is the rate constant?(c) Using the rate constant found in Part b, calculate the concentration of sucrose at 210 min if the initial sucrose concentration were 0.316 M
and the reaction were zero order in sucrose.

Part AThe reactant concentration in a zero-order reaction was 0.100 M after 200 s and 2.50×10−2 M after 335 s . What is the rate constant for this reaction?Express your answer with the appropriate units. Indicate the multiplication of units, as necessary, explicitly either with a multiplication dot or a dash.Part BWhat was the initial reactant concentration for the reaction described in Part A?Express your answer with the appropriate units. Indicate the multiplication of units, as necessary, explicitly either with a multiplication dot or a dash.Part CThe reactant concentration in a first-order reaction was 5.80×10−2 M after 25.0 s and 1.00×10−2 M after 75.0 s . What is the rate constant for this reaction?Express your answer with the appropriate units. Indicate the multiplication of units, as necessary, explicitly either with a multiplication dot or a dash.Part DThe reactant concentration in a second-order reaction was 0.870 M after 300 s and 7.00×10−2 M after 880 s . What is the rate constant for this reaction?Express your answer with the appropriate units. Indicate the multiplication of units, as necessary, explicitly either with a multiplication dot or a dash.

The reactionA → B + Cis known to be zero order in A and to have a rate constant of 5.0 x 10 -2 mol/L•s at 25°C. An experiment was run at 25°C where [A]0 = 1.0 x 10 -3 M.a. Write the integrated rate law for this reaction.

The decomposition of hydrogen iodide on finely divided gold at 150°C is zero order with respect to HI. The rate defined below is constant at 1.20 x 10-4 mol/L•s.a. If the initial HI concentration was 0.250 mol/L, calculate the concentration of HI at 25 minutes after the start of the reaction.

The evaporation of a 130-nm film of n-pentane from a single crystal of aluminum oxide was found to be zero order with a rate constant of 1.92 x 1013 molecules/cm2 at 120 K.If the initial surface coverage is 9.0 x 1016 molecules/cm2, how long will it take for one-half of the film to evaporate?

The evaporation of a 130-nm film of n-pentane from a single crystal of aluminum oxide was found to be zero order with a rate constant of 1.92 x 1013 molecules/cm2 at 120 K. What fraction of the film will be left after 12 s if the initial surface coverage is 8.9 x 1016 molecules/cm2?

A certain substance X decomposes. It is found that 50% of X remains after 100 minutes. How much X remains after 200 minutes if the reaction order with respect to X is zero order?

A certain substance, initially present at 0.0800 M, decomposes by zero-order kinetics with a rate constant of 2.50 x 10-2 mol/L•s. Calculate the time (in seconds) required for the system to reach a concentration of 0.0210 M.

A first-order decomposition reaction has a rate constant of 0.0029 yr^-1. How long does it take for [reactant] to reach 12.5% of its original value? Be sure to report your answer to the correct number of significant figures.

At a certain temperature, the half-life of the first order decomposition of phenol (shown below) is 1.94 hr.phenol → cyclopentadiene + carbon monoxideAnswer the following questions about the decomposition of phenol and report all answers to three significant figures.1. If the initial concentration of phenol is 4.89 times 10-4 M, calculate the time (in hr) required for the concentration of phenol to decrease to 27.5% of the initial concentration. 0.896 hr2. If the initial concentration of phenol is 4.89 times 10-4 M, calculate the concentration (in M) after 1.48 hr. 2.82*10-5 M

The gas phase decomposition of sulfuryl chloride at 600 K SO2Cl2(g) → SO2 (g) + Cl2(g) is first order in SO2Cl2. During one experiment it was found that when the initial concentration of SO2Cl2 was 4.42x10-3 M, the concentration of SO2Cl2 dropped to 1.02x10-3 M after 391 min had passed. Based on this experiment, the rate constant for the reaction is _____ min-1.

A wooden artifact from a Chinese temple has a 14^C activity of 42.0 counts per minute as compared with an activity of 58.2 counts per minute for a standard of zero age. From the half-life for 14^C decay, 5715 yr, determine the age of the artifact.

The data below show the concentration of N 2O5 versus time for the following reaction: N2O5 (g) → NO3 (g) + NO2 (g) Determine the value of the rate constant. Predict the concentration of N2O5 at 300 s.

The rate constant for this zero order reaction is 0, 0140 M s^-1 at 300 degree C.A ----> productsHow long (in seconds) would it take for the concentration of A to decrease from 0.940 M to 0.220 M

Enter your answer in the provided box.For the simple decomposition reaction AB (g) → A (g) + B (g) rate = k [AB]2 and k = 0.20 L/mol • s. If the initial concentration of AB is 1.50 M, what is [AB] after 16.9 s?

The rate constant for the reaction is 0.920 M-1. s-1 at 200°C.A → products If the initial concentration of A is 0.00220 M, what will be the concentration after 205 s?

Consider this reaction:2NH3 (g) → N2 (g) + 3H2 (g) At a certain temperature it obeys this rate rate = (0.318 s-1)[NH3] Suppose a vessel contains NH3 at a concentration of 1.26 M. Calculate the concentration of NH3 in the vessel 2.90 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits.

The isomerization of methylisonitrile to acetonitrile CH3NC (g) → CH3CN (g) is first order in CH3NC. The rate constant for the reaction is 9.45 x 10-5 s-1 at 478 K. The half-life of the reaction when the initial [CH3NC] is 0.030 M is _____________ s.

Cyclopentadiene (C5H6) reacts with itself to form dicyclopentadiene (C10H12). A 0.88 M solution of C5H6 is monitored as a function of time as the reaction proceeds. A graph of In[C6H5] versus time yields a straight line. How many seconds will it take for the [C6H5] to be 0.11 M The k for the reaction is 0.17 s-1.

After 48.0 min, 19.0% of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics?

The rate constant for this first-order reaction is 0.0590 s-1 at 400°C.A → productsAfter how many seconds will 18.3% of the reactant remain?

The rate constant for this second-order reaction is 0.800 M-1 s-1 at 300°C. A → products How long (in seconds) would it take for the concentration of A to decrease from 0.670 M to 0.310 M?

Be sure to answer all parts.The growth of Pseudomonas bacteria is modeled as a first-order process with k = 0.035 min -1 at 37°C. The initial Pseudomonas population density is 1.0 x 103 cells/L. Enter your answers in scientific notation. (a) What is the population density- after 4.0 h? (b) What is the time required for the population to go from 1.0 x 10 3 to 3.0 x 103 cells/L?

After 78.0 min, 33.0% of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics?

The rate constant for the reaction is 0.150 M-1 • s-1 at 200°C. A → products If the initial concentration of A is 0.00590 M, what will be the concentration after 735 s?

The reaction CH3-N≡C → CH3-C≡Nis a first-order reaction. At 230.3°C. k = 6.29 x 10-4 s-1. If [CH3-N≡C] is 1.00 x 10-3 initially, [CH3-N≡C) is ________ after 1.000 x 103 s. (a) 2.34 x 10-4(b) 4.27 x 10-3 (c) 1.00 x 10-6 (d) 1.88 x 10-3(e) 5.33 x 10-4

The rate constant for the reaction is 0.930 M-1• s-1 at 200°C. A → productsIf the initial concentration of A is 0.00980 M, what will be the concentration after 115 S? Determine the order of the reaction from the units on the rate constant. Then use the appropriate integrated rate equation. The integrated rate equation are

At a certain temperature this reaction follows first-order kinetics with a rate constant of 0.00285 s-1: 2Cl2O5 (g) → 2Cl2 (g) + 5O2 (g) Suppose a vessel contains Cl2O5 at a concentration of 0.640 M. Calculate the concentration of Cl2O5 in the vessel 280. seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits.

At a certain temperature the rate of this reaction is second order in H3PO4 with a rate constant of 10.3 M-1 • s-1. 2H3PO4 (aq) → P2O5 (aq) + 3H2O (aq) Suppose a vessel contains H3PO4 at a concentration of 1.29 M. Calculate the concentration of H3PO4 in the vessel 1.00 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits.

The reaction CH3-N=C → CH3-C=N is a first-order reaction. At 230°C, k = 6.29 x 10-4 s-1. If [CH3-N=C] is 1.00 x 10-3 initially, [CH3-N=C] is ___________ after 1.000 x 103 s.(i) 1.00 x 10-6(ii) 1.88 x 10-3 (iii) 2.34 x 10-4 (iv) 4.27 x 10-3 (v) 5.33 x 10-1

If a radioactive isotope has a rate constant for decay of 0.0650 min-1, what fraction of this isotope remains after 15.0 minutes?

The data below were collected for the following reaction at a certain temperature: X2Y → 2X + Y Determine the value of the rate constant at this temperature. What is the half-life for this reaction (at the initial concentration)? What is the concentration of X after 11.0 hours?Express your answer using two significant figures.

The rate constant for this first order reacion is 0.400 s-1 at 400°C.A → products How long (in seconds) would it take for the concentration of A to decrease from 0.600 M to 0.200 M?

After 54.0 min, 23.0% of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics?

Enter your answer in the provided box.The following reaction, 2A → B is first order in A and has a rate constant, k, of 7.5 x 10-3 s-1 at 110°C. With a starting concentration of [A] = 1.65M, what will [A] be after 3.5 min?

At a certain temperature the rate of this reaction is second order in H2CO3 with a rate constant of 4.5M-1s-1. H2CO3 (aq) → H2O (aq) + CO2 (aq)Suppose a vessel contains H2CO3 at a concentration of 0.800 M. Calculate how long it takes for the concentration of H2CO3 to decrease to 9.0% of its initial value. You may assume no other reaction is important. Round your answer to 2 significant digits.

The rate constant for this first-order reaction is 0.0950 s-1 at 400°C. A → products After how many seconds will 18.2% of the reactant remain?

A particular reactant decomposes with a half-life of 149 s when its initial concentration is 0.309 M. The same reactant decomposes with a half-life of 243 s when its initial concentration is 0.189 M. Determine the reaction order. What is the value and unit of the rate constant for this reaction?

The following reaction was monitored as a function of time: AB → A + B A plot of 1/[AB] versus time yields a straight line with slope 5.3 x 10 -2 (M • s)-1. Write the rate law for the reaction. What is the half-life when the initial concentration is 0.56 M? Express your answer using two significant figures.

A reaction of the form aA → Products gives a plot of In[A] vs time (in seconds) which is a straight line with a slope of -7.35 x 103. Assuming [A]o = 0.0100 M, calculate the time (in seconds) required for the reaction to reach 15.9 percent completion.

The gas phase decomposition of nitrogen dioxide at 383°C NO2 (g) → NO(g) + ½O2 (g) is second order in NO2 with a rate constant of 0.540 M-1s-1. If the initial concentration of NO2 is 0.361 M, the concentration of NO2 will be __________ M after 19.0 seconds have passed.

The first-order reaction, 2N2O(g) → 2N2(g) + O2(g), has a rate constant equal to 1.23 s -1 at 1000 K. How long will it take for the concentration of N2O to decrease to 92.46% of its initial concentration?

In a first order decomposition, the constant is 0.00309 sec-1. What percentage of the compounds has decomposed after 8.19 minutes?

The rate constant for this second-order reaction is 0.170 M-1 • s-1 at 300 °C. A → products How long (in seconds) would it take for the concentration of A to decrease from 0.700 M to 0.290 M?

The rate constant for this first-order reaction is 0.0680 s-1 at 400°C. A → products After how many seconds will 10.6% of the reactant remain?

The integrated rate laws for zero-, first-, and second-order reaction may be arranged such that they resemble the equation for a straight line, y = mx + b. Part CThe reactant concentration in a first-order reaction was 5.10 x 10-2 M after 20.0 S and 8.70 x 10-3 M after 75.0 S. What is the rate constant for this reaction? Express your answer with the appropriate units. Indicate the multiplication of units, as necessary, explicitly either with a multiplication dot or a dash. Part D The reactant concentration in a second-order reaction was 0.610 M after 210 s and 7.10 x 10-2 M after 785 S. What is the rate constant for this reaction?Express your answer with the appropriate units. Indicate the multiplication of units, as necessary, explicitly either with a multiplication dot or a dash.

In a study of the gas phase decomposition of hydrogen iodide at 700 K.HI (g) → 1/2H2 (g) + 1/2I2 (g) the following data were obtained: (1) The observed half life for this reaction when the starting concentration is 1.46 M is ______ s and when the starting concentration is 0.730 M is _______ s. (2) The average Δ(1/[HI])/Δt from t = 0 s to t = 768 s is _______ M-1 s-1. The average Δ(1/[HI])/Δt from t = 768 s to t = 2.30 x 103 s is ________ M-1 s-1. (3) Based on these data, the rate constant for this order reaction is ________ M-1 s-1.

Enter your answer in the provided box. For the simple decomposition reaction AB (g) → A (g) + B (g) race = k [AB]2 and k = 0.35 L/mol • s. How long will it take for [AB] to reach 1/3 of its initial concentration of 1.50 M?

The reaction 2NO2 → 2NO + O2 obeys the rate law: Δ[O2]/Δt = (1.40 x 10 -2 sec) [NO2]2 at 500. K. If the initial concentration of NO2 is 1.00 M, how long will it take for the [NO 2] to decrease to 14.2% of its initial value? A) 61.3 s B) 139 s C) 432 s D) 1.40 x 10-2 s E) cannot be determined from this data

The rate of decomposition of PH3 was studied at 851.00°C. The rate constant was found to be 0.0585 s-1. 4PH3 → P4 + 6H2 If the reaction is begun with an initial PH3 concentration of 0.95 M, what will be the concentration of PH3 after 28.50 s?

The rate constant for this first-order reaction is 0.510 s-1 at 400°C. A → products How long (in seconds) would it take for the concentration of A to decrease from 0.710 M to 0.270 M?

A reactant decomposes with a half-life of 193 s when its initial concentration is 0.205 M. When the initial concentration is 0.673 M, this same reactant decomposes with the same half-life of 193 s. What is the order of the reaction? • 0 • 1 • 2 What is the value and unit of the rate constant for this reaction?

Enter your answer in the provided box. A first-order decomposition reaction has a rate constant of 0.0032 yr-1. How long does it take for [reactant] to reach 12.5% of its original value? Be sure to report your answer to the correct number of significant figures.

The data below were collected for the following reaction at a certain temperature: X2Y → 2X + Y What is the half-life for this reaction (at the initial concentration)?What is the concentration of X after 13.0 hours? Express your answer using two significant figures.

After 40.0 min, 29.0% of a compound has decomposed. What is the half-life of this reaction assuming first order.

The active ingredient in an over the counter pain killer analgesic decomposes with a rate constant, k = 42.4 x 10-4 day-1. How many days does it take for 15% of the original ingredient to react? Report 2 significant digits.

In a first order decomposition, 83% of a compound is left after 92 minutes. What is the value of k for the reaction in min-1 (give answer to 5 decimal places)

Nitrous add (HNO2) slowly decomposes to NO, NO2 and water by the following second-order reaction: 2HNO2 (aq) → NO (g) + NO2 (g) + H2O (l) Use the data below to determine the rate law and the rate constant for this reaction: Determine the half-life for the decomposition of HNO2.

Consider the following initial rate data (at 281 K) for the decomposition of a substrate (substrate 1) which decomposes to product 1 and product 2: Determine the half-life for the decomposition of substrate 1 when the initial concentration of the substrate is 2.88 M.

Consider this reaction: 2Cl2O5 (g) → 2Cl2 (g) + 5O2 (g) At a certain temperature it obeys this rate law. rate = (6.48 M-1 • s-1)[Cl2O5]2 Suppose a vessel contains Cl2O5 at a concentration of 1.16 M. Calculate the concentration of Cl2O5 in the vessel 0.820 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits.

The reaction below is first order in [H2O2]: 2H2O2 (I) → H2O (I) + O2 (g) A solution originally at 0.600 M H2O2 is found to be 0.075 M after 54 min. The half-life for this reaction is ___________ min.

For the decomposition of nitrous oxide at 565°C, the rate of the reaction is determined by measuring the disappearance of N2O. 2N2O → 2N2 + O2 At the beginning of the reaction, the concentration of N 2O is 1.01 M. After 21.2 min the concentration has dropped to 0.419 M. What is the rate of the reaction?

In a study of the decomposition of hydrogen peroxide in dilute sodium hydroxide at 20°C. H2O2 (aq) →H2O (l) + 1/2O2 (g) the concentration of H2O2 was followed as a function of time. It was found that a graph of ln[H2O2] versus time in minutes gave a straight line with a slope of -1.61 x 10-3 min-1 and a y-intercept of -3.44. Based on this plot, the reaction is ______________ order in H2O2 and the half life for the reaction is ____________ minutes.

For A → products, time and concentration data were collected and plotted as shown here. Determine the reaction order, the rate constant, and the units of the rate constant.

At a certain temperature this reaction follows first-order kinetics with a rate constant of 0.892s-1: 2CI2O5 (g) → 2CI2 (g) + 5O2 (g) Suppose a vessel contains CI2O5 at a concentration of 1.02 M. Calculate the concentration of CI2O5 in the vessel 0.760 seconds later. You may no other reaction is important. Round your answer to 2 significant digits.

What is the half-life (in seconds) of a zero-order reaction which has an initial reactant concentration of 0.974 M with a k value of 5.42 x 10-2 M/s?

Consider this reaction:2N2O5 (g) → 2N2O4 (g) + O2 (g) At a certain temperature it obeys this rate law. rate = (0.00995 M-1 • s^-1)[N2O5]2 Suppose a vessel contains N2O5 at a concentration of 1.48 M. Calculate the concentration of N2O5 in the vessel 310. seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits.

The rate constant for the reaction is 0.230 M-1 • s-1 at 200°C. A → products If the initial concentration of A is 0.00540 M, what will be the concentration after 955 s?

The rate constant for the second-order reaction, 2NO2(g) → 2NO(g) + O2(g), is 0.54 M-1 s-1 at 300°C. (a) How long (in seconds) would it take for the concentration of NO2 to decrease from 0.62 M to 0.28 M? (b) Calculate the half-lives at these two concentrations.

Sodium-24, which is used to locate blood clots in the human circulatory system, has a half-life of 15.0 hours. A sample of sodium-24 with an initial mass of 17.5 g was stored for 60.0 hours. How many grams of sodium-24 is left in the sample after 60.0 hours?

The rate constant for a particular radioactive isotope is 0.0422 hr-1. Calculate the half-life of this isotope.

The reaction: 2HI → H2 + I2, is second order and the rate constant at 800 K is 2.162 M-1 s-1 How long will it take for 3.185 mol/L of HI to decrease to one-fourth of its initial concentration?

In a study of the decomposition of nitramide in aqueous solution at 25°C.NH2NO2 (aq) → N2O (g) + H2O (l) the concentration of NH2NO2 was followed as a function of time. It was found that a graph of ln[NH2NO2] versus time in seconds gave a straight line with a slope of -6.72 x 10-5 s-1 and a y-intercept of -0.863. Based on this plot, the reaction is ________ order in NH2NO2 and the rate constant for the reaction is _____________ s-1.

Enter your answer in the provided box. For the simple decomposition reaction AB (g) → A (g) + B (g) rate = k[AB]2 and k = 0.20 L/mol • s. If the initial concentration of AB is 1.50 M, what is [AB] after 10.2 s?

The first-order reaction SO2Cl2 → SO2 + Cl2 is 10% complete in 80 min. How long would it take for the reaction to be 95% complete? (a) 1.8 min (b) 104 min (c) 530 min (d) 2300 min (e) 990 min

The rate constant for the reaction is 0.620 M-1 s-1 at 200°C. A → products If the initial concentration of A is 0.00560 M, what will be the concentration after 775 s?

Consider the reactionC2H6 →2CH3at a temperature where the half-life is 15.8 minutes.What is the first order rate constant at this temperature?K = _____ min-1 How long would it take for the concentration of C2H6 to drop from 3.0 mM to 1.0 mN?T = _____ minIf the initial concentration is 3.0 mM? what would the concentration be after 28.0 minutes?[C2H6] = _____ mMHow long would it take to convert 95% of C2H6 at this temperature?t = _____ min

A particular reactant decomposes with a half-life of 119 s when its initial concentration is 0.303 M. The same reactant decomposes with a half-life of 239 s when its initial concentration is 0.151 M. Determine the reaction order. What is the value and unit of the rate constant for this reaction?

In a first-order decomposition reaction. 39.0% of a compound decomposes in 11.0 min. How long (in min) does it take for 87.1% of the compound to decompose? Enter to 2 decimal places.