Question

The vapour density of ${N_2}{O_4}$ at a certain temperature is 30. What is the percentage dissociation of $N{O_2}$ at that temperature?
(A) 53.3%
(B) 106.6%
(C) 26.7%
(D) 83.4%

Answer 1

Find out the vapour density of ${N_2}{O_4}$ initially before the reaction commences. Then find the degree of dissociation by taking the ratio of difference of initial VD and VD at equilibrium to VD at equilibrium.

Complete step by step answer:
-Vapour density: VD = Molar mass of gas / 2 (1)
-Degree of dissociation:
$\alpha = \dfrac{{D - d}}{d}$ (2)
Where, α = degree of dissociation,
D = density in the beginning of the reaction or theoretical (calculated) VD,
d = density at equilibrium or VD after dissociation (observed).

-On dissociation ${N_2}{O_4}$ leads to the formation of $N{O_2}$. This dissociation reaction can be written as: ${N_2}{O_4} \rightleftarrows 2N{O_2}$
-The molecular mass of ${N_2}{O_4}$ is = 2(14) + 4(16)
= 28 + 64 = 92

-We will now talk about vapour density. The density of any vapour in relation to hydrogen is known as vapour density (VD). Mathematically it can be written as:
VD = Molar mass of gas / molar mass of ${H_2}$
= Molar mass of gas / 2 (1)
-So, using equation (1) we can find out the vapour density of ${N_2}{O_4}$.
VD = Molar mass of ${N_2}{O_4}$ / 2
= $\dfrac{{92}}{2}$ = 46

-The vapour density of ${N_2}{O_4}$ in the beginning of the reaction is 46 and the question says that its vapour density at certain temperature (which means at equilibrium) is 30.
So, D = 46 and d = 30.

Let the degree of dissociation be α. So, using equation (2) we will find out the degree of dissociation.
$\alpha = \dfrac{{D - d}}{d}$
= $\dfrac{{46 - 30}}{{30}}$
= $\dfrac{{16}}{{30}}$ = 0.5333

In percentage form degree of dissociation will be = 53.33%
So, the correct answer is “Option A”.

Note: Do not get confused between density and vapour density. Density is the ratio of mass of some substance to its volume, while vapour density is the ratio of weight of certain volume of a gas to weight of an equal volume of hydrogen.
${N_2}{O_4}$ (Nitrogen tetroxide) is planar and can be stored as a liquid at room temperatures. It acts as a very powerful oxidizer and thus is used as one of the most important rocket propellants. In combination with a hydrazine based rocket fuel it is a hypergolic propellant.