Question

In a gaseous mixture at 20 degree Celsius the partial pressure of the components are ${H_2}$: 150 torr, $C{H_3}$: 300 Torr, $C{O_2}$:200 Torr , ${C_2}{H_4}$: 100 Torr. Volume % of ${H_2}$ ?
(A)26.67
(B)73.33
(C) 80.00
(D)20

Answer 1

Hint: We should know Dalton’s law of partial pressure and its application might help in better understanding of this concept. In order to solve this question, we should know the formula to calculate the volume percentage.

Complete step by step:
Firstly the partial pressure of gas is given by Roault’s law which states that the partial pressure of any volatile component of a solution at any temperature, is equal to the vapour pressure of the pure components multiplied by the mole fraction of that component in the solution.
According to this law, partial pressure of a component is given by:
 \[{P_x} = {x_x}P_x^ \circ \]
Where, ${p_x}$=partial pressure of component
$p_x^ \circ $ ${X_x}$ = mole fraction of component X
$p_x^ \circ $ = vapour pressure of pure component X.
Let ${P_A}$,${P_B}$ be the partial pressure of components A and B:
Partial pressure of the component A: \[{P_x} = {x_x}P_x^ \circ \]
Partial pressure of the component B: \[{P_B} = {x_B}P_B^ \circ \]
Let me introduce Dalton’s law of partial pressure which states that "total vapour pressure is equal to sum of partial pressure of all the components".
According to Dalton’s law of partial pressure: \[p = {p_A} + {p_B}\]
\[p = {p_A} + {p_B}\]
This is the main concept behind this question.
In the question already the partial pressure of each component are given, so we have to find out the total vapour pressure using Dalton’s law of partial pressure:
\[p = {p_{{H_2}}} + {P_{C{H_4}}} + {P_{C{O_2}}} + {P_{{C_2}{H_4}}}\]
\[P = 150 + 300 + 200 + 100\]
\[P = 750\]Torr
The volume percentage of a gas in mixture of gas is equation pressure of the particular gas divide by the total vapour pressure:
Volume % of a component = \[\dfrac{{partial{\text{ }}pressure{\text{ }}of{\text{ }}a{\text{ }}component\;}}{{Total{\text{ }}pressure}} \times 100\]
\[Volume{\text{ }}\% \;\;of\;{H_2} = \dfrac{{150}}{{750}} \times 100\]
Volume % of ${H_2}$= 20%

Thus, Option D is the correct answer.

Note: The Roaullt's law and the Dalton's law of partial pressure is very important remember, because it has many applications in solutions chapter. Dalton's law of partial pressure is based on Roault's law. Always while calculating the percentage of anything don't forget to multiply it by 100.