# A container has a volume of 7 L and holds 2 mol of gas. If the container is expanded such that its new volume is 15 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

##### 1 Answer
Jan 17, 2017

Increase the amount of gas to 4.29 mol by injecting another 2.29 mol.

#### Explanation:

We can use the ideal gas law for this, written in its proportionality form:

$\frac{{P}_{1} {V}_{1}}{{n}_{1} {T}_{1}} = \frac{{P}_{2} {V}_{2}}{{n}_{2} {T}_{2}}$

If temperature and pressure are to be held constant, ${P}_{1} = {P}_{2}$ and ${T}_{1} = {T}_{2}$, so these terms can be cancelled from the equation:

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

$\frac{7 L}{2 m o l} = \frac{15 L}{n} _ 2$

${n}_{2} = \frac{2 \left(15\right)}{7} = 4.29 m o l$