# Which gas has the greatest volume?

I was given $4$ gases, which gases had the same temperature ,pressure and mass and was told to determine the gas with the greatest volume.

The gases were $\ce{CH4}$, $\ce{NO}$, $\ce{C2H2}$ and $\ce{CO2}$.

So I assumed the mass was $1$ gram and used the formula $n=\frac{\text{mass}}{\text{molar mass}}$ and found that $\ce{NO}$ had the greatest volume but the correct answer given to me was $\ce{CH4}$.

I cannot find out where I went wrong?

• Check your molar masses and calculations. – jerepierre Jun 10 '17 at 13:43

First of all, if in a certain condition it is said that mass (or any other parameter) is constant, you cannot just assume ${1gm}$ (or any other number). Mass being constant means $\Delta m =0$, not that it is ${1gm}$. You have no way of knowing what the mass is (unless stated in the question, of course). The correct approach is to assume the mass to be $'m'\space{units}$. Now, this mass $'m'$ can assume any value, according to the condition.

Moving on, you have made a mistake while comparing molar mass and volume.

The ideal gas equation gives us the relation,

$$PV=\frac{\text{Mass}}{\text{Molar Mass}}RT$$

$$V=\frac{1}{\text{Molar Mass}}.\frac{(\text{Mass})RT}{P}$$
$$V\propto \frac{1}{\text{Molar Mass}}$$