consider equimolar samples of the same ideal gas at the same volume, but different temperatures. sample c is at a higher temperature than sample d.

The question is incomplete.

This is the complete question:

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

Compare the pressures. Compare the rms speeds. Compare the average kinetic energies.

pressure: A = B

RMS: A < B

kinetic energies: A = B

Explanation:

1) Pressure:

You can deal with this part of the question on the basis of Avogaro's principle which stated that equal volumes of gases at same temperature and pressure have the same number of particles (molecules).

Also, kinetic theory of gases postulates that the particles of gas are quited separated and in consequence the volume occupied by the particles of a gas is meaningless and does not influence the total volume occupied by a fixed number of particles.

Also, you can use the equation of ideal gases pV = nRT, from which p = nRT/V. if n, T, and V are fixed, then p is fixed.

The three approaches leads to the same conclusion.

Then, pressure of gas A is equal to pressure of gas B.

2) RMS

RMS stands for root mean square speed.

It is the room mean square speed of the particles of a gas.

the RMS is related with the temperature of the gas and the molar mass per this equation:

RMS = √(3RT/M), where R is the universal constant of gases, T is the absolute temperature and M is the molar mass.

Then, the greater the molar mass, the lower the RMS, which permits you conclude that the RMS of gas A is less than the RMS of the gas B.

3) kinetic energy

Temperature is a measure of the kinetic energy.

Equal temperatures of the gas means equal kinetic energies.

The Kinetic Molecular Theory states that the average energy of molecules is proportional to absolute temperature.

So, you conclude that the same amount of gases, at the same temperature, contain equal kinetic energies.