# A container has a volume of 15 L and holds 9 mol of gas. If the container is compressed such that its new volume is 8 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Sep 1, 2017

See below

#### Explanation:

$v = 15 L$
$n = 9$

According to Ideal Gas equation

$P V = n R T - - - - - - - - - - - \left(I\right)$

Where
$R$ is a constant whose value depends
$P$ is pressure
$V$ is volume
$n$ is moles
$T$ is temperature

$P 15 = 9 T R$

Now moving on to the second condition

$v = 8 L$
n = ?

$P V = n R T$

$P 8 = n R T - - - - - - - - - \left(I I\right)$

Dividing (I) and (II)

We have,

$\frac{P 15}{P 8} = \frac{9 R T}{n R T}$

Since the given conditions are same for both the cases, These can be canceled out..... So we are left with

$\frac{15}{8} = \frac{9}{n}$

$\frac{72}{15} = n$

$n = 4.8$

Therefore 9 - 4.8 moles need to be removed

i.e $4.2 m o l$ to maintain the same pressure and temperature.