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 15L15 L and holds 9mol9 mol of gas. If the container is compressed such that its new volume is 8L8 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?