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I came across the following question recently

Calculate the difference between two specific heat of 1 g of helium gas at NTP. Molecular weight of helium = 4 and J = $4.186×10^7$ erg $cal^{-1}$

The solution given is

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If R is called the “Universal” Gas constant why does it change for different molecular masses?

I found this website which talked about Gas constant vs. universal gas constant, but all the problems I’ve come across I’ve always used PV=nRT and haven’t had to consider the molecular weight. Why is this situation any different?

Could you please point out where I’m making a mistake or having a misconception on this topic?

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2 Answers 2

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but all the problems I’ve come across I’ve always used PV=nRT and haven’t had to consider the molecular weight. Why is this situation any different?

Because $R$ in the equation $PV=nRT$ is the universal gas constant, sometimes designated with an overhead bar as $\bar R$, is a single value that can be applied any ideal gas when the amount of the gas is given in moles ($n$).

On the other hand, for the equation

$$PV=mR_{g}T$$

where $m$ is the mass of the gas, $R_{g}$ is the specific gas constant. Since the number of moles of gas equals its mass divided by its molecular weight, the relationship between $\bar R$ and $R_g$ is

$$R_{g}=\frac{\bar R}{mol.wt}$$

Hope this helps.

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  • $\begingroup$ Just for clarification, “where m is the mass of the gas”, in the equation m is the mass? Not molecular weight? $\endgroup$
    – Natru
    May 9, 2022 at 15:37
  • $\begingroup$ @Natru Correct. $m$ is the mass, not the Molecular Weight. $\endgroup$
    – Bob D
    May 9, 2022 at 16:49
  • $\begingroup$ So, nR = mR_g like my downvoted answer ;) $\endgroup$
    – buddhabrot
    May 10, 2022 at 9:52
  • $\begingroup$ @buddhabrot yes. Have no idea why your answer was downvoted $\endgroup$
    – Bob D
    May 10, 2022 at 10:07
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$nR_{universal} = mR_{specific}$, so if you deal with amount of molecules you can use the universal gas constant in the ideal gas law.

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    $\begingroup$ Not sure why anyone downvoted this $\endgroup$
    – buddhabrot
    May 9, 2022 at 9:44

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