The crux of my question is, why is just the amount of particles included in $PV=nRT$ and there is nothing to account for the mass of the individual molecules? Or is mass accounted for in temperature, the average kinetic energy which includes mass in $\tfrac{1}{2}mv^2$.

Thanks in advance!

  • $\begingroup$ In reference to the title, If you do it, R would depend on the identity of the gas...; it doesnt happen in the ordinary equation (R is universal). $\endgroup$
    – user43021
    Sep 20 '18 at 0:53
  • $\begingroup$ Thanks, that makes sense. any idea on the answer to my second part however $\endgroup$
    – Adam
    Sep 20 '18 at 0:56
  • $\begingroup$ R would depend on the identity of the gas, and n would be the mass PV=mR'T $\endgroup$
    – user43021
    Sep 20 '18 at 0:59
  • $\begingroup$ Why in the world should the formula account for the color of my eyes? It shouldn't. Ditto for the mass of the molecule. $\endgroup$ Sep 20 '18 at 5:18
  • $\begingroup$ Change the formula to $pV=(m/M)RT$ and you have your mass in it. $m/M=n$ ! Pressure depends on the average impulse of every gas particle. $\endgroup$
    – Karl
    Sep 20 '18 at 7:27

The overall notion is that gases exhibit "ideal" behavior so that the identity of the particular gas molecule doesn't matter. Thus regardless of what compound the gas molecule is, or if the gas is a mixture of different compounds, a mole of gas molecules at standard temperature and pressure (STP, 0 °C and $1.000\times10^5$ Pa) occupies a volume of 22.7 liters. So the equation for an ideal gas is

$$PV = nRT$$

In addition, there is the Maxwell–Boltzmann distribution which is for the speed of molecules. The gist is that regardless of the compound, gas molecules have the same kinetic energy spread. Since kinetic energy is given by $mv^2/2$, that means that lighter molecules have faster speeds than heavier molecules.

If you try to define the relationship by the molecular weight of the gas, then the value of the gas constant, $R$ would be different for different compounds and/or mixtures. Now in reality the ideal gas law works reasonably well, but there are empirical equations which fit the relationship between P, V, and T better. For those empirical equations the extra coefficients are fitted to the experimental data for particular gas compound under consideration.


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