# Problem: Consider equimolar samples of different ideal gases at the same volume and temperature. Gas A has a higher molar mass than gas B.Consider equimolar samples of the same ideal gas at the same volume, but different temperatures. Sample A is at a higher temperature than sample B.Consider equimolar samples of the same ideal gas at the same temperature, but different volumes. Sample A has a larger volume than sample B.FOR ALL:Compare the pressures. Compare the rms speeds.Compare the average kinetic energies.

###### FREE Expert Solution

1. Consider equimolar samples of different ideal gases at the same volume and temperature. Gas A has a higher molar mass than gas B.
Comparing the pressures.

Ideal gas equation:

$\overline{)\mathbf{PV}\mathbf{=}\mathbf{nRT}}\phantom{\rule{0ex}{0ex}}\frac{\mathbf{P}\overline{)\mathbf{V}}}{\overline{)\mathbf{V}}}\mathbf{=}\frac{\mathbf{nRT}}{\mathbf{V}}\phantom{\rule{0ex}{0ex}}\overline{)\mathbf{P}\mathbf{=}\frac{\mathbf{nRT}}{\mathbf{V}}}$

• equimolar → equal moles (n)
• same volume (V)
• same temperature (T)

The pressure of gas A and gas B are equal.

Comparing the rms speeds.

$\overline{){\mathbf{\mu }}_{\mathbf{rms}}\mathbf{=}\sqrt{\frac{\mathbf{3}\mathbf{RT}}{\mathbf{M}}}}$

• 3 and R are constants.
• same temperature (T)

The molar mass (M) is in the denominator so the smaller the molar mass (M) of the gas, the larger the μrms would be.

molar mass gas A > molar mass gas B

The rms speed of gas B is greater than the rms speed of gas A.

Compare the average kinetic energies.

According to the kinetic molecular theory of gases, the average kinetic energy of a gas is directly proportional to the temperature of the gas: a higher temperature results in a higher average kinetic energy.

Gas A and gas B are at the same temperature.

The average kinetic energies of gas A and gas B are equal.

2. Consider equimolar samples of the same ideal gas at the same volume, but different temperatures. Sample A is at a higher temperature than sample B.

###### Problem Details

Consider equimolar samples of different ideal gases at the same volume and temperature. Gas A has a higher molar mass than gas B.

Consider equimolar samples of the same ideal gas at the same volume, but different temperatures. Sample A is at a higher temperature than sample B.

Consider equimolar samples of the same ideal gas at the same temperature, but different volumes. Sample A has a larger volume than sample B.

FOR ALL:

Compare the pressures.

Compare the rms speeds.

Compare the average kinetic energies.

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Kinetic Energy of Gases concept. If you need more Kinetic Energy of Gases practice, you can also practice Kinetic Energy of Gases practice problems.