Question

Q1.An ideal gas is contained in a cylinder at pressure P1 and temperature T1. The initial moles of the gas is n1. The gas leaks from the cylinder and attains a final pressure P2 and temperature T2. The new moles of the gas present in the cylinder is​

Answer 1

Explanation:

Given:

An ideal gas is contained in a cylinder at pressure P1 and temperature T1. The initial moles of the gas is n1. The gas leaks from the cylinder and attains a final pressure P2 and temperature T2.

To find:

New moles of gas in cylinder?

Calculation:

Since the gas is ideal , we can say that it will follow the IDEAL GAS EQUATION:

$P1 \: V1 =( n1)R \: (T1)$

Now, at different system conditions:

$P2 \: V2 = (n2)R \: (T2)$

Now, divide the Equations:

$\implies \: \dfrac{P2 \: V2}{P1 \: V1} = \dfrac{(n2) \: T2}{(n1) \: T1}$

$</p><p>\implies \: n2 = \bigg( \dfrac{P2 \: V2}{P1 \: V1} \times \dfrac{(n1)(T1)}{T2} \bigg)$

So, final answer is:

$\boxed{ \bf\: n2 = \bigg( \dfrac{P2 \: V2}{P1 \: V1} \times \dfrac{(n1)(T1)}{T2} \bigg)} </p><p>$

Answer 2

Final/New number of moles =n2

n2=P2V/RT2

By ideal gas equation

PV=nRT

n=PV/RT

Let V be volume of cylinder

initial number of moles

n1=P1V/RT1

final number of moles

n2=P2V/RT2

{ note : volume of cylinder remains the same}

so

to find number of moles leaked=n2-n1