Question

A vessel of volume $V$ contains a mixture of ideal gases at temperature $T .$ The gas mixture contains $n_{1}, n_{2}$ and $n_{3}$ moles of three gases. Assuming ideal gas system, the pressure of the mixture is

• A. $\frac{\left(n_{1}+n_{2}+n_{3}\right) R T}{V}$
• B. $\frac{\left(n_{1} n_{2} n_{3}\right) R T}{V}$
• C. $\frac{R T}{\left(n_{1}+n_{2}+n_{3}\right) V}$
• D. $\frac{R T}{V\left(n_{1} n_{2} n_{3}\right)}$

Answer 1

Answer: (A)

By Dalton's law of partial pressure, pressure of mixture of three gases,
$p=p_{1}+p_{2}+p_{3}$
According to the ideal gas equation,
$p V =n R T$
$p =\frac{n R T}{V}$
Temperature $T$ and volume $V$ are same for all three gases, but number of moles are different,
i.e. $n_{1},\, n_{2}$ and $n_{3}$.
So, $p=\frac{n_{1} R T}{V}+\frac{n_{2} R T}{V}+\frac{n_{3} R T}{V}$
$p=\frac{\left(n_{1}+n_{2}+n_{3}\right) R T}{V}$