Question

A vessel of volume 16.6 litres containing an ideal gas at 47°C and
pressure 150 kPa is allowed to leak till the pressure falls to 102 kPa
at the same temperature. The number of moles of the gas leaked
during the process is​

Answer 1

MB=4MA

hope this will help you

Answer 2

Given:

A vessel of volume 16.6 litres containing an ideal gas at 47°C and pressure 150 kPa is allowed to leak till the pressure falls to 102 kPa at the same temperature.

To find:

Moles of gas leaked ?

Calculation:

Let's calculate the initial moles:

$\therefore \: PV = nRT$

$\implies \: (150 \times {10}^{3} ) \times 16.6 = n(8.31)(47 + 298)$

$\implies \: (150 \times {10}^{3} ) \times 16.6 = n(8.31)(345)$

$\implies \: n = 868.5 \: moles$

We know that for an IDEAL GAS :

$\therefore \: PV = nRT$

• As per the question, the temperature remains constant. Since the vessel volume will always remain same, V becomes constant.

$\implies \: \dfrac{P}{n} = constant$

$\implies \: \dfrac{P1}{n1} = \dfrac{P2}{n2}$

$\implies \: \dfrac{150}{n} = \dfrac{102}{n2}$

$\implies \: n2 = n \times \dfrac{102}{150}$

$\implies \: n2 = 0.68(n)$

So, number of moles lost

$\implies \: \Delta n= n - 0.68(n)$

$\implies \: \Delta n= 0.32(n)$

$\implies \: \Delta n= 0.32(868.5)$

$\implies \: \Delta n= 277.9 \: moles$

So, number of moles leaked is 277.9 moles.