Practice: Calculate the molar mass, in g/mol, of a gaseous compound with an average root mean velocity of 652 m/s at a temperature of 30o C.
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Increasing the temperature allows a gas to absorb thermal energy and convert into kinetic energy. Kinetic energy allows the gas to move and the speed at which it moves gives us the root mean square speed.
Root Mean Square Speed & Kinetic Energy
Concept #1: Understanding kinetic energy & Root Mean Square Speed
Transcript
Welcome back guys. In this new video, we're going to take a look at the kinetic energy of gases. We've talked about kinetic energy really quickly in previous videos. We say that when we increase the temperature of any type of container, the gas particles in there will absorb that thermal energy and convert it to kinetic energy. This is the energy that they're going to use in order to push themselves around inside of this container.
We're going to say in order to measure the average kinetic energy of a gas molecule or particle, we must employ the root mean square equation. The root mean square equation is U, which stands for velocity, equals square root of 3RT over M. When I say velocity, I mean speed. The units for velocity or speed are meters per second.
Here this R is not the same R we're used to seeing. Because we're talking about speed or energy, R is now 8.314 joules over moles times K. Remember when do I use this R? I use this R anytime we're talking about speed, velocity, kinetic energy. Energy is the key word here. The three keywords we look out for are energy speed or velocity. That's when we use this R. The other R is associated with the Ideal Gas Law. It's different.
Here, T represents temperature in Kelvin. Here, capital M means molar mass or molecular mass. But here it's different. We're used to seeing molecular mass or molar mass in grams per mole, but in this case, in this equation, it's going to be in kilograms per mole. You have to remember that. It's in kilograms per mole.
Now the R we're going to look at it a little bit closer. We're going to say here joules is just a form of energy. We're going to say joules are kilograms times meters squared over seconds squared. That's what joules mean. That means that our R is really 8.314 kilograms times meters squared over moles times K times seconds squared. Because the second squared is on the bottom here, we would have to put it on the bottom here. Just remember the units that are involved with joules. This is going to help us in our calculations to see what we isolate when we find our answer.
Example #1: A 1.56 x 1013 pg gaseous particle travels at 6.21 m/s. Determine its kinetic energy.
The kinetic energy (in J or kJ) of a gas molecule is directly proportional to its absolute temperature in Kelvins.
Remember that using the root mean square speed equation deals with molar mass in g/mol, so further conversion may sometimes be needed.
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Additional Problems
What is the root mean square speed (in m/s) of hydrogen molecules at 25.0°C?
( R= 8.3145 kg m2 s-2 mol -1 k-1)
a) no given answer is close
b) 3.72 x 106
c) 6.10 x 101
d) 1.93 x 103
e) 3.72 x 103
The root mean square speed of nitrogen molecules in air at 20°C is 511 m/s in a certain container. If the gas is allowed to expand to twice its original volume, the root mean square velocity of nitrogen molecules drops to 325 m/s. Calculate the temperature after the gas has expanded.1. 45.1°C2. −45.1°C3. 261°C4. 347◦C5. −347°C6. −261°C7. 154°C8. −154°C
Which gas will have the highest root mean square velocity at the same temperature?NH3 b) He c) CO2 d) SO2 e) NO2
A 0.81 mole sample of CO2 is confined in a 20 L container. The volume of the gas sample is decreased to 10L while holding temperature constant. The average molecular speed will.a. increaseb. decreasec. remain the samed. insufficient information to answer
The root-mean-square speed of gas molecules is 256.0 m/s at a given T. The gas has a molar mass of 32.00 g/mol. What would be the root-mean-square speed for a gas with a molar mass of 131.0 g/mol?a. 126.5 m/sb. 62.53 m/sc. 518.0 m/sd. 1048 m/se. 189.8 m/s
Calculate the root mean square velocity of nitrogen molecules at 25.0 °C. (1 kg = 1000 g)A) 729 m/s B) 515 m/s C) 149 m/s D) 16.29 m/s E) 51.2 m/s
What is the root mean square velocity (m/s) of H2O steam at 373 K?A) 2.26B) 22.7C) 71.4D) 372E) 719
Identify the gas particle that would travel the fastest at a temperature of 293 K.A. SO2B. CO2C. N2D. NeE. Ar
What is the root mean square speed of carbon dioxide molecules at 98°C? 1. 45.6 m · s -12. 574 m · s -13. 236 m · s -14. 459 m · s -15. 153 m · s -1
Helium is the lightest noble gas in the air. Calculate its root-mean-square speed (in m/s) in the winter when it is 0oC outside. (R = 8.3145 kg m 2 s -2 mol -1 K -1)a. 1845b. 1305c. 1.71 x 103d. 1.70 x 106e. 41.3
Calculate the root mean square velocity of nitrogen molecules at 25 °C.
A 1-L sample of CO initially at STP is heated to 546 K, and its volume is increased to 2 L.(c) What is the effect on the root mean square speed of the molecules?
Calculate the most probable speed of Cl2 molecules at 315 K .
Helium (He) is the lightest noble gas component of air, and xenon (Xe) is the heaviest. [For this problem, use R = 8.314 J/(mol·K) and express ℳ in kg/mol.](a) Find the rms speed of He in winter (0.°C) and in summer (30.°C).
The rms (root-mean-square) speed of a diatomic hydrogen molecule at 50°C is 2000 m/s. Note that 1.0 mol of diatomic hydrogen at 50°C has a total translational kinetic energy of 4000 J.(A) Diatomic oxygen has a molar mass 16 times that of diatomic hydrogen. The root-mean-square speed vrms for diatomic oxygen at 50°C is:(B) The total translational kinetic energy of 1.0 mole of diatomic oxygen at 50°C is:(C) The temperature of the diatomic hydrogen gas sample is increased to 100°C. The root-mean-square speed vrms for diatomic hydrogen at 100°C is: i. (16)(4000 J) = 64000 J ii. (4)(4000 J) = 16000 Jiii. 4000 Jiv. (1/4)(4000 J) = 1000 Jv. (1/16)(4000 J) = 150 Jvi. (√2)(2000 m/s) = 2800 m/s vii. (2)(2000 m/s) = 4000 m/s viii. (1/√2) (2000 m/s) = 1400 m/six. (1/2)(2000 m/s) = 1000 m/s
A gas is at 24°C. To what temperature must it be raised to triple the rms speed of its molecules?
Consider the following gases, all at STP: Ne, SF6, N2, CH4.Which one has the highest root-mean-square molecular speed at a given temperature?
The root mean square speed of H2 molecules at 25 °C is about 1.6 km/s. What is the root mean square speed of a N2 molecule at 25 °C?
Calculate the rms speed of CO molecules at 315 K .
Fill in the blanks for the following statement:The rms speed of the molecules in a sample of H2 gas at 300K will be ____ times larger than the rms speed of O2 molecules at the same temperature, and the ratio urms(H2)urms(O2) large{frac {u_{ m rms} ( m H_2)}{u_{ m rms}( m O_2)}} _____ with increasing temperature.a) four, will not changeb) four, will increasec) sixteen, will not changed) sixteen, will decreasee) not enough information is given to answer this question
At which set of conditions listed below will the atoms be moving the fastest?(a) Ne at 100°C(b) Ar at 100°C(c) Ne at 50°C(d) Ar at 50°C(e) the conditions in answers (a) and (b) and (c) and (d) will be the same speeds
You have a sample of gas at -32 oC. You wish to increase the rms speed by a factor of 2.To what temperature should the gas be heated?
At 300K, what is the correct ordering (from slowest to fastest) of average molecular speed of the following gases: Ar, HBr, SO2, and CO2?A) HBr < SO2 < CO2 < ArB) Ar < CO2 < SO2 < HBrC) Ar < HBr < SO2 < CO2D) HBr < CO2 < SO2 < ArE) All these gases have the same average speed at the same temperature
Calculate the root-mean-square speed of methane, CH4 (g), at 78 °C. (a) 23 m/s (b) 350 m/s(c) 550 m/s (d) 667 m/s (e) 739 m/s
What is the rms speed of He atoms at 295 K?
Calculate the rms speed of an oxygen gas molecule, O2, at 33.0?CExpress your answer numerically in meters per second.
Which of the following gases will have the largest root mean square speed at 100 °C?1. water2. argon3. oxygen4. methane 5. nitrogen
How is the root mean square velocity of a gas related to its molar mass?
Calculate the root mean square velocity of gaseous xenon atoms at 25 oC.
Calculate the root-mean-square velocity of CO2 at 286 K .
Calculate the root-mean-square velocity of CO at 286 K .
Calculate the root-mean-square velocity of SO3 at 286 K .
Calculate the root mean square velocity of I2(g) at 377 K.
Calculate the root mean square velocities of CH4(g) and N2(g) molecules at 273 K and 546 K.
At what temperature will He atoms have the same Crms value as N2 molecules at 25°C? Solve this problem without calculating the value of Crms for N2. Crms is the root mean square speed.
Which of the following gases will have the smallest root mean square speed at 100°C?(A) H2O (B) CH4(C) N2(D) O2(E) Ar
Mars has an atmosphere composed almost entirely of carbon dioxide, with an average temperature of -63°C.What is the rms speed of a molecule in Mars' atmosphere? Assume R = 8.315 J/mol•K.Express your answer to two significant figures and include the appropriate units.
Of these gases, which has the fastest-moving molecules (on average) at a given temperature?a. HBrb. NO2c. C2H6d. they all have the same average speed
What is the ratio of urms to ump for a sample of O2(g) at 300 K?
WF6 is one of the heaviest known gases.How much slower is the root-mean-square speed of WF6 than He at 300 K?
Calculate the rms speed of Cl2 molecules at 315 K .
Calculate the
most probable speed of an ozone molecule in the stratosphere,
where the temperature is 270 K.
How does the approximate root mean square
velocity of neon compare to that of krypton at the same temperature?
Calculate the rms speed of NF3 molecules at 28oC.
Calculate the rms speed of an oxygen gas molecule, O2, at 21.0 °C.Express your answer numerically in meters per second.In a given sample of gas, the particles move at varying speeds. The root mean square speed (rms speed) of particles in a gas sample, u, is given by the formulau=3RTMwhere T is the Kelvin temperature, M is the molar mass in kg/mol, and R = 8.314 J/(mol ⋅ K) is the gas constant. Effusion is the escape of gas molecules through a tiny hole into a vacuum.The rate of effusion of a gas is directly related to the rms speed of the gas molecules, so it's inversely proportional to the square root of its mass. The rms speed is related to kinetic energy, rather than average speed, and is the speed of a molecule possessing a kinetic energy identical to the average kinetic energy of the sample.Given its relationship to the mass of the molecule, you can conclude that the lighter the molecules of the gas, the more rapidly it effuses. Mathematically, this can be expressed aseffusion rate∝1mThe relative rate of effusion can be expressed in terms of molecular masses mA and mB asrate of gas A effusionrate of gas B effusion=mBmA
Consider separate 1.0-L samples of He(g) and UF6(g), both at 1.00 atm and containing the same number of moles. What ratio of temperatures for the two samples would produce the same root mean square velocity?
What is the ratio of urms to ump for a sample of O2(g) at 300 K? Will this ratio change as the temperature changes?
What is the ratio of urms to ump for a sample of O2(g) at 300 K? Will it be different for a different gas?
Consider the following drawing.If curves A and B refer to two different gases, He and O2 at the same temperature, which curve corresponds to He?
Consider the following drawing.If A and B refer to the
same gas at two different temperatures, which represents the
higher temperature?
Consider the following drawing.For each curve, which speed is highest:
the most probable speed, the root-mean-square speed, or
the average speed?
Find the rms speed of the molecules of a sample of N2 (diatomic nitrogen) gas at a temperature of 33.3°C
The average kinetic energy of the molecules in a gas sample depends only on the temperature, T. But given the same kinetic energies, a lighter molecule will move faster than a heavier molecule. rms speed = √3RT/M where R=8.314 J/(mol • K) and M is molar mass in kilograms per mole. Note that a joule is the same as a kg • m2/s2. What is the rms speed of N2 molecules at 287 K?What is the rms speed of He atoms at 287 K?
Calculate the root mean square velocity of F2,Cl2, and Br2 at 302 K .
Calculate the most probable speed of CO molecules at 315 K .