Question

What is the V.D. of $S{O_2}$ w.r.t. ${C_2}{H_4}$ ?
(A) 32
(B) 2.3
(C) 4

Answer 1

Hint: The formula to find the vapor density of the gas is as follows
\[{\text{Vapour density = }}\dfrac{{{\text{Molecular weight of the gas}}}}{{{\text{Molecular weight of hydrogen gas}}}}{\text{ }}\]

Complete Step-by-Step Solution:
Here, V.D stands for vapour density. We need to give the vapour density of $S{O_2}$ gas with respect to ${C_2}{H_4}$ gas.
- Vapour density is calculated relation to that of hydrogen gas. Vapour density of the gas is defined as the ratio of the mass of the gas divided by the same volume of hydrogen gas.
So, we can write the formula of vapour density of the gas with respect to its molecular weight and molecular weight of hydrogen as
\[{\text{Vapour density = }}\dfrac{{{\text{Molecular weight of the gas}}}}{{{\text{Molecular weight of hydrogen gas}}}}{\text{ }}....{\text{(1)}}\]
We know that the molecular formula of hydrogen gas is ${H_2}$.
So, molecular weight of ${H_2}$ = 2(atomic weight of H) = 2(1) = 2$ gm mo{l^{ - 1}}$
Now, we will first find the value of vapour pressure of sulphur dioxide gas with respect to hydrogen gas. Then we will find the same for ${C_2}{H_4}$ gas. Then we will compare them both in order to find the answer.
 For $S{O_2}$, Molecular weight = Atomic weight of S + 2(Atomic weight of O)
Molecular weight = 32 + 2(16) = 64$ gm mo{l^{ - 1}}$
Molecular weight of ${C_2}{H_4}$= 2 (Atomic weight of C) + 4 (Atomic weight of H)
Molecular weight = 2(12) + 4(1) = 24+4 = 28$ gm mo{l^{. - 1}}$
Now, we can find the vapour density of both the gases.
 For $S{O_2}$, putting the available values into equation (1), we get
\[{\text{Vapour density = }}\dfrac{{64}}{2} = 32\]
For ${C_2}{H_4}$, if we put the available values into equation (1), we get
\[{\text{Vapour density = }}\dfrac{{28}}{2} = 14\]
Now, we can write that vapour density of $S{O_2}$ with respect to ${C_2}{H_4}$ is $\dfrac{{32}}{{14}} = 2.3$
Thus, we can say that correct answer is 2.3

So, the correct option is (B).

Note: Note that vapour density is a unitless quantity as it is the ratio of two molecular weights. We can say that if the vapour density of a gas A is x with respect to B gas, then we can say that gas A is x times heavier than gas B.