Question

A 0.477 mol sample of O2 ​ gas has a volume of 12.1 L at a certain temperature and pressure. If all this O2 ​ were converted to ozone (O3 ​) at the same temperature and pressure, what is the ozone volume (in liters)? 3O2 ​ (g) → 2O3 ​ (g)

Answer 1

If we are assuming ideal behavior, then the Ideal Gas Equation, $PV = nRT$, is very helpful. The number of moles $n$ changes here by a factor of $\frac{2 \ mol \ O_3 }{3 \ mol \ O_2}$, so you have $0.318 \ mol \ O_3$. 

So, $V_1 = \frac{n_1RT_1}{P_1}$ and $V_2 = \frac{n_2RT_2}{P_2}$. Looking at the given information, P and T are constant (as is R, always). So, we can write $\frac{n_1}{V_1} = \frac{n_2}{V_2}$. Solving for $V_2$, we get $\frac{V_1n_2}{n_1}$. Then we plug in 12.1 L for $V_1$, $0.318 \ mol$ for $n_2$ and $0.477 \ mol$ for $n_1$. Thus $V_2 = 8.07 \ L \ O_3$.