Question

Dalton’s law of partial pressures is not applicable for which mixture of gases ?

• A. $H_2$ and $C{l}_2$
• B. $H_2$ and $S{O}_2$
• C. $H_2$ and $C{O}_2$
• D. $C{O}_2$ and $C{l}_2$

Answer 1

The correct option is A $H_2$ and $C{l}_2$

Dalton's law is applicable only to a mixture of non-reacting gases. As $H_2$ and $C{l}_2$ gases may react with each other to produce $HCl$ gas, Dalton's Law is not applicable.

Theory:

Dalton's Law of partial pressure:

The total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressures of the individual gases.

Partial Pressure: It is the pressure exerted by a constituent gas of the gaseous mixture when kept alone in the same container.

Consider there are three non-reacting constituting gases 1, 2 and 3 whose partial pressures are $P_1,P_{2}and{P}_3$ respectively at temperature T and volume V. Then, mathematically, Dalton's Law of partial pressure can be written:

$P_1=\frac{\left(n_{1}RT\right)}{V}$

$P_2=\frac{\left(n_{2}RT\right)}{V}$

$P_3=\frac{\left(n_{3}RT\right)}{V}$

$P_T=P_1+P_2+P_3$

$P_T=\frac{(n_1+n_2+n_3)\left(RT\right)}{V}$

$n_1+n_2+n_3=n_t=\text{total number of moles}$

$P_T=n_t\left(\frac{RT}{V}\right)$

$P_T=P_1+P_2+P_3$ (at constant T, V)

where, $P_{Total}=\text{Total pressure exerted by the mixture of gases}$.

This law is only applicable for mixture of non-reacting gases

Note : It is also applicable for the reacting gases which are in chemical equilibrium.

By diving $\frac{P_1}{P_T},\frac{P_2}{P_T}and\frac{P_1}{P_T}$

We get :$\frac{P_1}{P_T}=n_1/n_T={\chi }_1$ (mole fraction of 1st gas)

$\frac{P_2}{P_T}=n_2/n_T={\chi }_2$(mole fraction of 2nd gas)

$\frac{P_3}{P_T}=n_3/n_T={\chi }_3$(mole fraction of 3rd gas)