Question

The unit of equilibrium constant $K$ for the reaction \[A+B\rightleftharpoons C~\] would be
A. $mol.lite{{r}^{-1}}$
B. $mo{{l}^{-1}}litre$
C. mol. litre
D. Dimensionless

Answer 1

Hint: To solve this question we have to know about equilibrium constant and unit of equilibrium constant. In an equilibrium reaction the rate constant of the reaction is given as the ratio of concentration of product to the concentration of reactant. Any coefficient of the reactant or product is used as the power of the concentration. The unit of concentration is given as $mol.lite{{r}^{-1}}$.

Complete Step by Step Answer:
The given reaction is \[A+B\rightleftharpoons C~\].
Here one mole of reactant $A$ reacts with two moles of reactant $B$ to produce one mole of product $C$. It is a not an unimolecular reaction as the change in number of moles is not zero. It is an equilibrium reaction as the product can also decompose to give back the reactants.
Thus the equilibrium constant is given as-
$K=\dfrac{[C]}{[A][B]}$
The concentration of reactant and product has the unit of $mol.lite{{r}^{-1}}$ .
$K=\dfrac{mol.lite{{r}^{-1}}}{{{(mol.lite{{r}^{-1}})}^{2}}}$
$K=mo{{l}^{(1-2)}}.lite{{r}^{(-1+2)}}$
$K=mo{{l}^{-1}}.litre$
Thus the unit of equilibrium constant is $mo{{l}^{-1}}.litre$.
Thus the correct option is B.

Note: Units of equilibrium constant K will depend on the equilibrium of the concentration of the number of reactants to the products. If the total number of moles of product is equal to the total number of moles of reactant then the equilibrium constant K has no units i.e. it is dimensionless.