Question

A mixture of hydrogen and oxygen at one bar pressure contains 20% by weight of hydrogen. Partial pressure of hydrogen will be?
(A) $0.2\,\,bar$
(B) $0.4\,\,bar$
(C) $0.6\,\,bar$
(D) $0.8\,\,bar$

Answer 1

To find the partial pressure of hydrogen we need to calculate the mole fraction of Hydrogen by calculating the moles of Hydrogen and Oxygen. Partial pressure will be calculated by multiplying the mole fraction into peer pressure.

Formula Used
$No.\,\,of\,moles = \dfrac{{Given\,mass}}{{Molar\,mass}}$
$Partial\,pressure = mole\,fraction\,\, \times \,pure\,pressure$
$Mole\,fraction = \dfrac{{moles\,\,of\,component\,A}}{{moles\,of\,component\,A + moles\,of\,component\,B}}$
COMPLETE STEP-BY-STEP SOLUTION:
We are given hydrogen $20\%$ by weight. It means in a mixture of $100\,gm$. $20g$ is hydrogen.
Hence, Mass of Hydrogen $= 20g$ and Mass of Oxygen $= 80g$
The molar mass of Hydrogen $= 2g$ and Molar mass of oxygen $= 32\,g$.
Now, we will calculate the moles of hydrogen gas which is given as;
$\Rightarrow Moles{{ }}of\,hydrogen = \dfrac{{given\,mass\,of\,hydrogen}}{{molar\,mass\,of\,hydrogen}}$
$\therefore Moles{{ }}of\,hydrogen = \dfrac{{20}}{2} = 10$
Similarly, we will calculate the moles of oxygen gas which is given as;$\Rightarrow Moles{{ }}of\,oxygen = \dfrac{{given\,mass\,of\,oxygen}}{{molar\,mass\,of\,oxygen}}$
$\therefore Moles{{ }}of\,oxygen = \dfrac{{80}}{{32}} = 2.5$
Now, we will calculate the mole fraction of hydrogen from the above-written formula;
$\Rightarrow Mole\,fraction\,\,of\,hydrogen = \dfrac{{moles\,\,of\,hydrogen}}{{moles\,\,of\,hydrogen + moles\,\,of\,oxygen}}$
Mole Fraction of hydrogen $\Rightarrow \,({\chi _{hydrogen}}) = \dfrac{{10}}{{10 + 2.5}} = \dfrac{{10}}{{12.5}} = 0.8$
Now, we will calculate the partial pressure using the value of ${\chi _{hydrogen}}$.$Partial\,pressure = mole\,fraction\,\, \times \,pure\,pressure$
$Partial\,pressure = 0.8\,\, \times \,1 = 0.8$
Hence, Partial pressure of hydrogen at $1$ bar pressure is $0.8\,\,bar$
Therefore, Option (D) is correct.

Additional Information
Mole fraction is a way used to express the concentration of a solution. It is represented by the number of moles of a particular component present in a mixture divided by the total number of moles in that mixture.

Note:
The partial pressure of a gas is a parameter of the thermodynamic activity of that gas molecule. In a mixture of gases, every constituent gas has a partial pressure which is the notional pressure of that gas. Dalton’s law states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by the gases separately in the mixture. It is dependent on the mole fraction of the gases.