# A container has a volume of 8 L and holds 1 mol of gas. If the container is expanded such that its new volume is 9 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Jun 2, 2016

$1.125$ mol.

#### Explanation:

The law of the perfect gasses says:

$P V = n R T$

where $P$ is the pressure, $V$ is the volume, $n$ is the number of mol $R$ is the constant of the perfect gas and $T$ is the temperature.

At the beginning ${V}_{i} = 8$ L and ${n}_{i} = 1$ mol while at the end ${V}_{f} = 9$ L. We want that all the quantities except $n$ stay constant. So we can write the two equations such as

$P {V}_{i} = {n}_{i} R T$
$P {V}_{f} = {n}_{f} R T$

and we can divide the first for the second:

$\setminus \frac{P {V}_{i}}{P {V}_{f}} = \setminus \frac{{n}_{i} R T}{{n}_{f} R T}$

Only the quantities with index $i$ or $f$ changes, the other are constant, so we can cancel them

${V}_{i} / {V}_{f} = {n}_{i} / {n}_{f}$ and substituting the numbers

$\frac{8}{9} = \frac{1}{n} _ f$ and then

${n}_{f} = \frac{9}{8} = 1.125$ mol.