Final answer:
The molar kinetic energy of 0.3 mol of helium will be the same as that of 0.4 mol of argon at 400 K, which is 400 K. This is because the kinetic energy for an ideal gas is only dependent on the temperature.
Step-by-step explanation:
The question is asking at what temperature the molar kinetic energy of 0.3 mol of helium (He) will be the same as that of 0.4 mol of argon (Ar) at 400 K. The key concept here is that, for an ideal gas, the kinetic energy of the gas molecules depends only on the temperature, and not on the amount of substance or type of molecule.
According to the equipartition theorem, the average kinetic energy of a gas molecule (KE) is proportional to the absolute temperature (T) and can be expressed as:
KE = (3/2) * k * T
where k is Boltzmann's constant. Since the temperature is the only factor that affects the kinetic energy in this case, the temperature at which the molar kinetic energy of 0.3 mol of He is the same as that of 0.4 mol of Ar at 400 K will also be 400 K.
It doesn't matter how much of each gas we have, whether it's 0.3 mol or 0.4 mol, as long as we're comparing the same kinds of particles (in this case, individual gas atoms). Therefore, if 0.4 mol of argon has the same kinetic energy at 400 K, then 0.3 mol of helium will also have the same kinetic energy at that same temperature.