Question

In what mass ratio, $S{O_2}$ and ${N_2}$ should be mixed so that partial pressure exerted by gases is the same?
(A). $7:20$
(B). $7:40$
(C). $16:7$
(D). $40:7$

Answer 1

Hint: While the development in the study of gaseous states, two types of gases were discovered namely the ideal gas and the real gas. Given the question, we are dealing with the laws of the ideal gas equation. The ideal gas equation is given by $PV = nRT$ where $P$ is pressure, $V$is volume, $n$ is the gaseous moles, $R$ is universal gas constant and $T$ is temperature. The ideal gas equation is given by Robert Boyle, Jacques A.C Charles, and Joseph Gay-Lussac.

Complete answer:
Let the mass of the given gases $S{O_2}$ and ${N_2}$ be $M$ .
The number of $S{O_2}$ would be given as $\dfrac{M}{{64}}$ .
In the similar fashion the number of ${N_2}$ would be given as $\dfrac{M}{{28}}$ .
Let the partial pressure of any gas say $S{O_2}$ is ${P_A}$ and that of other gas ${N_2}$ is ${P_B}$ .
Then for one gas; ${P_A} = \dfrac{M}{{64}}(\dfrac{{RT}}{V})$
And for another gas ${P_B} = \dfrac{M}{{28}}(\dfrac{{RT}}{V})$
Now, $\dfrac{{{P_B}}}{{{P_A}}} = \dfrac{M}{{28}} \times \dfrac{{64}}{M}$
$\Rightarrow \dfrac{{{P_B}}}{{{P_A}}} = \dfrac{{64}}{{28}} = \dfrac{{16}}{7}$
Or the ratio is $16:7$.

Therefore, the required ratio is $16:7$. So, option (C) is correct.

Note:
The total pressure of any given mixture of gases is equal to the sum of the partial pressure of all the given gases in the mixture. Partial pressure helps us in predicting the movement of gases. This is so because gases tend to equalize their pressure in two regions that are connected. Since, each of the given gas in a mixture behaves independently of the other gases, we can therefore use the ideal gas law to calculate the partial pressure of each gas in the mixture.