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

According to Raoult's law, partial pressure of each component present in a solution consisting of volatile liquids is directly proportional to its mole fraction. The expression of Raoult’s law is $p = {p^0}x$. Here, p is the partial pressure of the component in the solution, ${p^0}$ is the partial pressure of the pure component and x is mole fraction.

Complete step by step answer:
Here, to calculate partial pressure of hydrogen, we have to use Raoult’s law. To use Raoult’s law, we need mole fraction of hydrogen and pressure of hydrogen (pure).

Given that mass of oxygen is 20%, that means, 100 g of mixture contains 20 g of hydrogen. So,
Mass of hydrogen=20 g

Mass of oxygen=100-20=80 g

Now, we have to calculate the mole number of both oxygen and hydrogen. The formula to calculate number of moles is,

${\rm{Number}}\,{\rm{of}}\,{\rm{moles}} = \dfrac{{{\rm{Mass}}}}{{{\rm{Molar mass}}}}$
…… (1)
For oxygen, mass is 80 g and molar mass=$2 \times 16 = 32\,{\rm{g}}\,{\rm{mo}}{{\rm{l}}^{ - 1}}$
. So, using equation (1),

$\Rightarrow {\rm{Moles}}\,{\rm{of}}\,{\rm{oxygen}} = \dfrac{{80}}{{32}} = 2.5\,{\rm{mol}}$

Similarly for hydrogen mass is 20 g and molar mass=$2 \times 1 = 2\,{\rm{g}}\,{\rm{mo}}{{\rm{l}}^{ - 1}}$

$\Rightarrow {\rm{Moles}}\,{\rm{of}}\,{\rm{hydrogen}} = \dfrac{{20}}{2} = 10\,{\rm{mol}}$

Now, we calculate moles fraction of hydrogen.

${\rm{Mole}}\,{\rm{fraction}}\,{\rm{of}}\,{\rm{hydrogen}} = \dfrac{{{\rm{Moles}}\,{\rm{of}}\,{\rm{hydrogen}}}}{{{\rm{Moles}}\,{\rm{of}}\,{\rm{hydrogen}} + {\rm{Moles}}\,{\rm{of}}\,{\rm{oxygen}}}}$

$\Rightarrow {\rm{Mole}}\,{\rm{fraction}}\,{\rm{of}}\,{\rm{hydrogen = }}\dfrac{{10}}{{10 + 2.5}} = \dfrac{{10}}{{12.5}} = 0.8$

The pressure of hydrogen is given as 1 bar and mole fraction of hydrogen is 0.8. So, we have to put these values in Raoult’s law expression to calculate partial pressure of hydrogen.

$p = {p^0}x$

$\Rightarrow p = 1 \times 0.8\,{\rm{bar}} = {\rm{0}}{\rm{.8}}\,{\rm{bar}}$

Therefore, partial pressure of hydrogen is 0.8 bar.

Hence, correct answer is option D.

Note:
Henry’s law states that the solubility of gas in a liquid depends on the pressure of the gas. There are many real life examples where Henry’s law is applied. For example, in soda water and soft drinks, solubility of carbon dioxide is increased by sealing the bottle under high pressure.