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Question: A gaseous mixture contains 56 g of \[{N_2}\]​ , 44 g of \[C{O_2}\]​ and 16 g of \[C{H_4}\] . The tot...

A gaseous mixture contains 56 g of N2{N_2}​ , 44 g of CO2C{O_2}​ and 16 g of CH4C{H_4} . The total pressure of the mixture is 720 mm of Hg. The partial pressure of methane is
A.75 mmHg
B.100 mmHg
C.180 mmHg
D.215 mmHg

Explanation

Solution

We know that according to Raoult’s Law we can say that partial pressure of a gas in a mixture of gas is equal to the product of the total pressure of the system and the mole fraction of that particular gas. Thus to find out the partial pressure of methane we need to find out the total number of moles in the mixture and in turn the mole fraction of methane.

Complete answer:
To find out the total number of moles of a given substance we need to apply the given formula:
⇒Number of moles = MassMolar mass\Rightarrow {\text{Number of moles = }}\dfrac{{Mass}}{{Molar{\text{ }}mass}}
We can thus find the number of moles of N2{N_2} , CO2C{O_2} and CH4C{H_4} by using this equation.
⇒Number of moles (N2) = 56g28gmol−1=2moles\Rightarrow {\text{Number of moles (}}{{\text{N}}_2}{\text{) = }}\dfrac{{56g}}{{28gmo{l^{ - 1}}}} = 2moles
⇒Number of moles (CO2) = 44g44gmol−1=1 mole\Rightarrow {\text{Number of moles (C}}{{\text{O}}_2}{\text{) = }}\dfrac{{44g}}{{44gmo{l^{ - 1}}}} = 1{\text{ }}mole
⇒Number of moles (CH4) = 16g16gmol−1=1 mole\Rightarrow {\text{Number of moles (C}}{{\text{H}}_4}{\text{) = }}\dfrac{{16g}}{{16gmo{l^{ - 1}}}} = 1{\text{ }}mole
Thus we can say that the total number of moles of substance found in the gaseous mixture is 2+1+1 which is equal to 4 moles.
Now we can say that the mole fraction of methane will be given by the formula:
⇒Mole fraction of CH4 = Number of moles of CH4Total number of moles in the mixture \Rightarrow {\text{Mole fraction of C}}{{\text{H}}_4}{\text{ = }}\dfrac{{{\text{Number of moles of C}}{{\text{H}}_4}}}{{T{\text{otal number of moles in the mixture}}}}{\text{ }}
⇒Mole fraction of CH4 = 14\Rightarrow {\text{Mole fraction of C}}{{\text{H}}_4}{\text{ = }}\dfrac{1}{4}
We know that Partial pressure of methane = Total pressure ×\times Mole fraction of methane
Thus we can say that
⇒PCH4=720×14\Rightarrow {P_{C{H_4}}} = 720 \times \dfrac{1}{4}
⇒PCH4=180 mmHg\Rightarrow {P_{C{H_4}}} = 180{\text{ }}mmHg
Thus we can say that the correct option is (C).

Note:
The same quantities can be used to find out the partial pressure of carbon dioxide or nitrogen. When asked to find out a different quantity we can just substitute the value of the mole fraction of that particular gas in the equation that we have used. This is an alternative way in which the question might be framed.