# A container has a volume of 9 L and holds 18 mol of gas. If the container is expanded such that its new volume is 54 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Nov 18, 2016

The answer is $= 90 m o l$

#### Explanation:

Let's work with the ideal gas equation $P V = n R T$

With the initial conditions,

${P}_{1} {V}_{1} = {n}_{1} R {T}_{1}$

With the final conditions,

${P}_{1} {V}_{2} = {n}_{2} R {T}_{1}$

as the temperature and the pressure do not change,

From those 2 equations,

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

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

${V}_{1} = 9 l$

${V}_{2} = 54 l$

${n}_{1} = 18 m o l$

${n}_{2} = 54 \cdot \frac{18}{9} = 108 m o l$

Number of moles of gas to be injected $= {n}_{2} - {n}_{1}$

$= 108 - 18 = 90 m o l$