Question

For the reaction,
\[A{B_{2(g)}} \to A{B_{(g)}} + {B_{(g)}}\]
If is negligible, then degree of dissociation () of is proportional to: (multiple correct options)
A. \[\dfrac{1}{P}\]
B. \[\dfrac{1}{V}\]
C. \[\dfrac{1}{{\sqrt P }}\]
D. \[\sqrt V \]

Answer 1

Hint: If << 1, then it can be neglected when performing addition and subtraction. Also, the equilibrium constant of a reaction depends only on temperature and is independent of the quantities of reactants and products, the presence of a catalyst and the presence of an inert material.

Complete step by step answer:
For our convenience, let the number of moles of \[A{B_2}\] at t = 0 be 1. When the equilibrium is reached, the number of moles of \[A{B_2}\] decomposed is equal to and the number of moles formed in the product side will be times their stoichiometric value. It can be represented in a chemical equation as:
\[A{B_{2(g)}} \to A{B_{(g)}} + {B_{(g)}}\]
At equilibrium, the number of moles of = 1-, while the number of moles of AB and B formed is as their stoichiometric values are 1.
Therefore, their equilibrium constant is equal to
\[K = \dfrac{{{{({M_{AB}})}^1}{{({M_B})}^1}}}{{{{({M_{A{B_2}}})}^1}}}\]
 \[K = \dfrac{{\dfrac{\alpha }{V} \times \dfrac{\alpha }{V}}}{{\dfrac{{1 - \alpha }}{V}}}\]
As << 1, therefore 1-1. Therefore, the above equation simplifies to:
\[K = \dfrac{{{\alpha ^2}}}{V}\]
So,
\[\alpha = \sqrt {KV} \]…. Say eq.1
And as, PV=nRT
If temperature is constant, which in turn is during a chemical reaction, then
\[V = \dfrac{k}{P}\]; where k is a constant…. Say eq.2
Therefore, using equation 2 in equation 1, we get
\[\alpha = \sqrt {\dfrac{K}{P}} \]

Hence, the degree of dissociation is directly proportional to the square root of volume and is inversely proportional to the square root of pressure of the gas.

Therefore, the correct options are (C) \[\dfrac{1}{{\sqrt P }}\] and (D) \[\sqrt V \]

Note: A student can often mistake the concentrations in the formula of equilibrium constant for moles. It must be remembered to use the concentrations in the formula of equilibrium constant.