| MadSci Network: Chemistry |
In fact, given a constant temperature, pressure, and volume, the number of molecules (or moles) is not constant for different gases. You may have been told this in introductory chemistry, however, this is only an approximation based on the ideal gas law. Real gases have inter and intra-molecular forces (fugacity, viscosity, mass volume, etc) that make the ideal gas approximation fail at high pressures and temperatures. However, given conditions that do not violate the assumptions of the ideal gas law, the number of molecules per unit volume (also called number density) for different type molecules can be considered constant. You were on the right track about the "lighter" molecules moving faster and 'heavier" molecules moving slower, effectively exerting the same force per unit area. Now the average kinetic (translational) energy is found by the temperature of the gas. I pause here because it's more complicated depending on whether you're talking about monoatomic or polyatomic gases. If you want the full 9 yards, I refer you to Paul Atkin's Physical Chemistry textbook. Anyway, since the temperature is the same for two gases, the average KE is the same. It's roughly equal to kt (k is Boltzmann's constant in units of J/K). k is equal to nR so: E= nRT n=E/RT Now recall the ideal gas law: PV = nRT so E = PV or P = E/V So for gasses, pressure can be thought of as a gauge of how much energy there is in a given volume. Since two gases of the same temperature have the same energy, if they occupy the same volume, they must also have the same pressure.
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