# 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.