# Calculating volume % in a mixture of gases at equilibrium

In a mixture of $\ce{N2}$ and $\ce{H2}$ initially In a mole ratio of $1:3$ at $\ce{30 atm}$ and $\pu{300^\circ C}$, the percentage of ammonia by volume under the equilibrium is $17.8$. I have to calculate the equilibrium constant $K_\mathrm p$ of the mixture for the reaction $$\ce{N2(g) + 3H2(g)<=>2NH3(g)}$$

When I read the question, the first thing that comes to me is Dalton's law of partial pressure and (I think) that according to that law we can imagine the components of gaseous mixture occupying a volume ($V$) each equal to the total volume of container. Thus, that is why we simply write the partial pressure of any gas as ($P_iV=n_iRT$) and sum all the partial pressure to get total pressure.

Coming back to original question, according to the previous logic, each gas in the container at equilibrium is occupying same volume ($V$) equal to the total volume of the container. Then the term volume % doesn't make any sense because each gas is occupying the whole volume of the container (under ideal gas assumptions) so volume% of each gas $= 100\%$.

So what does the question mean by "Volume %" (for gases)? Is there any flaw in the above logic?

P.S: I would have easily solved the question if mole % was given as each gas has different moles so no problem there.

• I know it doesn't make sense, but, when the term volume percent is used, it means mole percent. – Chet Miller Apr 18 '17 at 15:27
• @Chester Miller if we mean mole percent then why do we even bother to use the term volume percent ?? I just can't think of any logic for doing so .. it feels so Bizarre to me to think that any serious chemistry teacher or book writers will use such terms so lightly and then don't even mention that they actually meant something else .. Making situations troublesome for weak students like me ( Another Reason got added to my list of why I don't like chemistry ) – Freelancer Apr 18 '17 at 18:27
• Anyway thank-you for pointing out a small thing which was troubling me for quite some time.. – Freelancer Apr 18 '17 at 18:28
• I can't answer your questions because it never made sense to me either. In atmospheric science, they talk about "volume mixing ratio." It took me a while to realize that this is the same thing as mole fraction. Go figure! – Chet Miller Apr 18 '17 at 18:55
• Perhaps "volume %" is meant to distinguish from "weight %" (or mass %), and the question simply assumes that you will remember that the volume of one mole of gas is the same as the volume of a mole of another gas (because we are not even thinking of solids or liquids). – James Gaidis Feb 24 '18 at 17:39