Question

A storage tank contains $2$ moles of $Ar,3$ moles of $O_2$, $5$ moles of $N_2$. If volume of tank is $1{\text{m}}^3$, find the total pressure exerted by mixture of gases at $300\text{K}$?

• A. $24942{\text{N/m}}^2$
• B. $22000{\text{N/m}}^2$
• C. $21000{\text{N/m}}^2$
• D. $23500{\text{N/m}}^2$

Answer 1

The correct option is A $24942{\text{N/m}}^2$

According to Dalton's law of partial pressure,
$P_{\text{net}}=P_1+P_2+P_3+...+P_n$
Here,
$P_{\text{net}}=P_{Ar}+P_{O_2}+P_{N_2}$
and
Volume $\left(V\right)=1{\text{m}}^3$
We know,
$PV=nRT$
$\therefore P_{Ar}\times 1{\text{m}}^3=2\times RT$
Similarly,
$P_{O_2}\times 1{\text{m}}^3=3\times RT$
$P_{N_2}\times 1{\text{m}}^3=5\times RT$

$\therefore P_{\text{net}}=P_{Ar}+P_{O_2}+P_{N_2}$
$\Rightarrow P_{net}=2RT+3RT+5RT$
$\Rightarrow P_{net}=(2+3+5)\times R\times T$
$\Rightarrow P_{net}=10\times 8.314\times 300{\text{N/m}}^2$
$\Rightarrow P_{net}=24942{\text{N/m}}^2$