# Question #6715e

Dec 7, 2014

The answer is $4.46 L$.

First, let's try and anticipate what will happen. Nothing is said about pressure and temperature, so wel'll assume they stay constant. Now, given the fact that the number of moles increases, we would expect the volume to increase as well, since we now have more moleculs present.

Starting from the ideal gas law, $P V = n R T$, and considering an initial state and a second state, we could write

$P {V}_{1} = {n}_{1} R T$ (1) and $P {V}_{2} = {n}_{2} R T$ (2). DIviding (1) by (2) (or the other way around, it isn't that important), we get

${V}_{1} / {V}_{2} = {n}_{1} / {n}_{2}$

Therefore, ${V}_{2} = {n}_{2} / {n}_{1} \cdot {V}_{1} = \frac{\left(0.129 + 0.072\right) m o l e s}{0.129 m o l e s} \cdot 2.86 L = 4.46 L$, which matches our initial prediction of ${V}_{2} > {V}_{1}$.