Question

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

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:

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

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

So, final answer is:

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

Answer 2

Explanation:

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

P1 \: V1 =( n1)R \: (T1)P1V1=(n1)R(T1)

Now, at different system conditions:

P2 \: V2 = (n2)R \: (T2)P2V2=(n2)R(T2)

Now, divide the Equations:

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

P1V1

P2V2

=

(n1)T1

(n2)T2

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

P1V1

P2V2

×

T2

(n1)(T1)

)

So, final answer is:

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

n2=(

P1V1

P2V2

×

T2

(n1)(T1)

)