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

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Answer 1 · 2017-09-01T02:17:39

See below

$v = 15 L$ $v= 15L$
$n = 9$ $n = 9$

According to Ideal Gas equation

$P V = n R T - - - - - - - - - - - (I)$ $PV = nRT-----------(I)$

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

$P 15 = 9 T R$ $P15 = 9TR$

Now moving on to the second condition

$v = 8 L$ $v = 8L$
$n = ?$ $n = ?$

$P V = n R T$ $PV = nRT$

$P 8 = n R T - - - - - - - - - (I I)$ $P8 = nRT --------- (II)$

Dividing (I) and (II)

We have,

$\frac{P 15}{P 8} = \frac{9 R T}{n R T}$ $(P15)/(P8) = (9RT)/(nRT)$

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

$\frac{15}{8} = \frac{9}{n}$ $(15)/(8) = (9)/(n)$

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

$n = 4.8$ $n = 4.8$

Therefore 9 - 4.8 moles need to be removed

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

A container has a volume of 15 L15L15 L and holds 9 mol9mol9 mol of gas. If the container is compressed such that its new volume is 8 L8L8 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?