# A container has a volume of 12 L and holds 15 mol of gas. If the container is expanded such that its new volume is 21 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Nov 29, 2016

The moles of gas to be injected into the container is 26.25 moles.

#### Explanation:

Take the ideal gas equation
$P V = n R T$
Considering the pressure and temperature as constants:
$V \propto n$
Volume of the gas is proportional to the number of moles of the gas.
By this we get,
$\frac{{V}_{1}}{{V}_{2}} = \frac{{n}_{1}}{{n}_{2}} \implies {n}_{2} = \frac{{V}_{2} \times {n}_{1}}{{V}_{1}}$
Substituing the values we get,
the moles of gas that to be injected into the container to maintain a constant temperature and pressure ${n}_{2} = 26.25 m o l$.