Question

For the equilibrium $N_2 + 3H_2\rightleftharpoons 2NH_3$ at 1000K is $2.37\times {{10}^{-3}}$ . If at equilibrium $\left[ {{N}_{2}} \right]=2M$, $\left[ {{H}_{2}} \right]=3M$, the concentration of $N{{H}_{3}}$ is:
(A) 0.00358 M
(B) 0.0358 M
(C) 0.358 M
(D) 3.58 M

Answer 1

Hint: An equilibrium constant (K) is the relationship between the concentration of reactants and products present at equilibrium in a reversible chemical process at a given temperature. It is represented as the ratio of the concentration of products and reactants.

Formula Used: For the reaction: $A + 3B \rightleftharpoons 2C$
The equilibrium constant is given by $K=\frac{{{[C]}^{2}}}{[A]{{[B]}^{3}}}$
In this question, the value of the equilibrium constant and the concentration of the reactants are given. We have to find the concentration of the product.

Complete Step by Step Answer:
The given equation is:
$N_2 + 3H_2\rightleftharpoons 2NH_3$
The given equilibrium constant for this reaction is $K=2.37\times {{10}^{-3}}$
The product and reactant concentrations are,$\left[ {{N}_{2}} \right]=2M$, $\left[ {{H}_{2}} \right]=3M$
The equilibrium constant is given by $K=\frac{{{[N{{H}_{3}}]}^{2}}}{[{{N}_{2}}]{{[{{H}_{2}}]}^{3}}}$
$2.37\times {{10}^{-3}}=\frac{{{[N{{H}_{3}}]}^{2}}}{[2]{{[3]}^{3}}}$
${{\left[ N{{H}_{3}} \right]}^{2}}=2.37\times {{10}^{-3}}\times 2\times 27$
${{[N{{H}_{3}}]}^{2}}=12.79\times {{10}^{-2}}$
$[N{{H}_{3}}]=\sqrt{12.79\times {{10}^{-2}}}$
$[N{{H}_{3}}]=0.358M$
Thus, the concentration of $N{{H}_{3}}$ is 0.358 M.
Correct Option: (C) 0.358 M.

Additional Information: Chemical equilibrium is a state in which the rates of both the forward and backward reactions are equal and the concentration of both the reactants and products is constant. At equilibrium, there is no net change in the number of moles, although conversion from reactants to products or products to reactants is still occurring. According to the law of mass action, the value of the equilibrium constant, K_c, is constant at a constant temperature. The concentrations of reactants and products may vary, but the value for K_c remains the same.

Note: The equilibrium constant should always be calculated after balancing the equation. The stoichiometric coefficients of each of the reactants or products should be carefully written as the powers of concentration of each substance.