$C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that for hydrogen gas $C_p - C_v = a$ and for nitrogen gas $C_p - C_V = b$ . The correct relation between a and b is? [JEE mains 2017]
I applied Mayers relation and used $C_p - C_v=R$ for all gases, hence $a=b$ but that formula seems to be incorrect here. Supposedly, the correct mayer's relation is given as:
$$ C_p -C_v = \frac{R}{M}$$
Where $M$ is molar mass of gas in consideration.
I don't get how this equation came about. I had written a derivation for this Mayer's relation as a self answer (see here) in one of my old posts but I can't see where in the derivation missed a factor of molecular mass.
So, my question is where does molar mass of gas come into the formula of Mayer's relation from?