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 H2O and CO2 as products. If the initial [C2H6] is 4.12 M, what is the concentration after 1.12 x 10-3 minutes?
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 25oC, 2 NOBr (g) ----> 2 NO (g) + Br2 (g). The rate of the reaction is found to be: rate = k [NOBr]2. The constant at 25oC is 7.80 x 10-4 M-1 s-1. If 0.550 moles of HBr (g) is placed in a 5.0 L container, how long will take for the concentration to reach 0.063 moles of HBr (g)?
Practice: In a typical chemical reaction, nitrogen trioxide, NO3, reacts to produce nitrogen dioxide, NO2, and oxygen gas, O.
2 NO3 (g) 2 NO2 (g) + 2 O (g)
A plot of [NO3] vs. time is linear and the slope is equal to 0.183. If the initial concentration of NO3 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.