Question

Check all the true statements concerning two identical containers, one with helium gas in it and one with xenon gas. Choose one or more:
a. When the temperature of either sample of gas increases, the root-mean-square speed increases.
b. If both gases are at the same temperature, they have the same average kinetic energy.
c. When the temperature of either sample of gas increases, the number of particles with average kinetic energy increases.
d. If both of the containers are at the same temperature, they will have the same root-mean-square speed.

Answer 1

Answer:

The answers to the question are as follows

a. True

b. True

c. True

d. false

Explanation:

The requiredrelation is

$u_{rms} = \sqrt{\frac{3RT}{m} }$

Where R = The gas constant

T =  the temperature in kelvin

m = molecular mass

$u_{rms}$ = root mean square speed

From the above relation on the kinetic energy of a gas we have the following true statements

a. When the temperature of either of the sample of gas increases, the root-mean-square speed increases.

This statement is true as the root means square velocity is directly proportional to the square root of the temperature a. is true

b. If both gases are at the same temperature, they have the same average kinetic energy.

From the equation for the average kinetic energy $KE_{avg} = \frac{3}{2} RT$ we see that the kinetic energy is directly proportional to its Kelvin temperature and  hence b. is true

c. When the temperature of either sample of gas increases, the number of particles with average kinetic energy increases.

This statement is true as shown in the kinetic energy equation

d. If both of the containers are at the same temperature, they will have the same root-mean-square speed.

This statement is false as xenon and helium have different, molecular masses