Question

State dalton's law of partial pressure .derive its mathematical form.

Answer 1

Dalton's law of partial pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases

$P_{total}=P_A+P_B+P_C.....$

The ideal gas law equation

$pV=nRT$

Lets say we have m components in the gas mixture, with number of moles of each being n₁, n_2, n₃,..., n_m. Let n denote sum of all moles. Let partial pressure of each be p₁ , p₂ , p₃,..., p_m, and p denote the total pressure.

From the gas law, we get:

$pV=nRT\newline pV=(n_1+n_2+n_3+...+n_m)RT\newline pV=n_1RT+n_2RT+n_3RT+...+n_mRT\newline pV=p_1V+p_2V+p_3V+...+p_mV\newline p=p_1+p_2+p_3+...+p_m$