Question

One litre of gas of mass, $2g$ at $300K$ and $1$ atm pressure, the pressure is made $0.75$ atm, at which of the following temperatures will one litre of the same gas have mass of one gram.

• A. $450K$
• B. $600K$
• C. $800K$
• D. $900K$

Answer 1

The correct option is A $450K$

The right option is 1

We have,

$P_1=1atm$

$V_1=1L$

$P_2=0.75atm$

$V_2=1L$

$W_1=1g$

$T_1=300k$

We know that,

According to the Gas equation,

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

$\frac{P_1{V}_1}{T_1}=\frac{n_{1}RT}{n_{2}R{T}_2}=\frac{W_{1}R{T}_1}{W_{2}R{T}_2}$

Therefore,

$\frac{P_1{V}_1}{P_2{V}_2}=\frac{W_{1}R{T}_1}{W_{2}R{T}_2}$

$1\times \frac{1}{0.75\times 1}=\frac{2\times 300}{1\times T_2}$

$T_2=2\times 300\times 0.75$

$=450K$