Question

A mixture of $He$ and $S{O_2}$ ​ at one bar pressure contains 20% by weight of $He$. Partial pressure of $He$ be:
A.0.2 bar
B.0.4 bar
C.0.6 bar
D.0.8 bar

Answer 1

Partial pressures is defined as the mole fraction of the gas in the mixture, and the total pressure of the gaseous mixture is the sum of the partial pressure of each component gas, given by$P = {P_1} + {P_2} + {P_3} + ........{P_n}$.

Complete step by step answer:
According to the question,
The percentage weight of helium is $20\%$
So in 100 gm of mixture, its proportion will be = $\dfrac{{20}}{{100}} \times 100 = 20$ gm
Similarly the proportion of $S{O_2}$ in the mixture will be = $100 - 20 = 80$ gm
Now we will calculate the moles of $He$ and $S{O_2}$,
Formula used to calculate the number of moles is;
Number of moles =$\dfrac{{given{\text{ }}mass}}{{atomic{\text{ }}mass}}.........(1)$
We know that atomic number of helium is 2 so its mass will be double the value of atomic number, i.e. 4
And similarly for $S{O_2}$, its atomic mass will be equal to the sum of the mass of its constituents.
So Atomic mass of $S{O_2}$ will be = mass of $S$ + mass of $2O$
Atomic mass of $S{O_2}$ = $32 + 2 \times 16$
Atomic mass of $S{O_2}$ = $64$
Now substituting the values in equation 1
Number of moles of helium = $\dfrac{{20}}{4}$
Number of moles of helium = $5$
Similarly for $S{O_2}$,
Number of moles = $\dfrac{{80}}{{64}}$
Number of moles = $1.25{\text{ }}mol$
To find the partial pressure of helium, we need its mole fraction;
Mole fraction of helium = $\dfrac{5}{{6.25}}$
Mole fraction of helium = $0.8$
So the partial pressure will be = $mole{\text{ }}fraction{\text{ }} \times {\text{ }}pressure{\text{ }}at{\text{ }}1{\text{ }}bar$
Partial pressure = $0.8{\text{ }} \times {\text{ }}1{\text{ }}bar\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}\;{\text{ }}$
Partial pressure $= {\text{ }}0.8{\text{ }}bar$

So, the correct answer is “Option D”.

Note:
The application of partial pressure measurement of a gas is a measure of its thermodynamic activity. The partial pressure of the gas is dependent upon temperature and its concentration, with increase in its concentration and temperature, is partial pressure can be increased.