Question

The equilibrium \[{\text{A}}\left( {\text{g}} \right) + 4{\text{B}}\left( {\text{g}} \right) \rightleftharpoons {\text{A}}{{\text{B}}_4}\left( {\text{g}} \right)\] is attained by mixing equal moles of A and B in a one litre vessel. Then at equilibrium
A.\[\left[ {\text{A}} \right] = \left[ {\text{B}} \right]\]
B.\[\left[ {\text{A}} \right] > \left[ {\text{B}} \right]\]
C.\[\left[ {\text{A}} \right] < \left[ {\text{B}} \right]\]
D.\[\left[ {{\text{AB}}} \right] > \left[ {\text{A}} \right]\]

Answer 1

Hint: Assume the initial number of moles as x. Proceed the reaction at equilibrium by considering the stoichiometric coefficient and we will get the relation between the concentrations.

Complete step by step solution:
Let us assume that the initial number of moles are x. Since it is given that the number of mole of both the reactants are same so we can write the number of moles initially present when the time is zero as:
\[{\text{time A}}\left( {\text{g}} \right) + 4{\text{B}}\left( {\text{g}} \right) \rightleftharpoons {\text{A}}{{\text{B}}_4}\left( {\text{g}} \right)\]
\[{\text{t}} = 0{\text{ x }} + {\text{ x}}\]
Let y moles of reactant A be reacted. For one mole of A, 4 moles of B are reacted. So for y moles of A 4y moles of B will be reacted.
\[{\text{t}} = {{\text{t}}_{{\text{eq}}}}{\text{ x}} - {\text{y }} + {\text{ x}} - 4{\text{y y}}\]
Concentration is defined as the ratio of number of moles to the volume of solution. Here the volume is one litre so the number of moles will be equal to the concentration.
It is clear from the equation that the number of moles of A is more than the number of moles of B. So the \[\left[ {\text{A}} \right] > \left[ {\text{B}} \right]\]

Hence, the correct option is B.

Note:
Equilibrium is a state when the concentration of all the species becomes equal. Here the rate of forward reaction becomes equal to the rate of backward reaction. This means that the rate at which the reactants convert to the product become equal to the rate at which product converting back to the reactant at equilibrium. Stoichiometry is defined as the minimum number of moles of the reacting species that is required to precede a reaction. It should not be confused with the number of moles.