Question

In the reaction, $H_{2(g)}+I_{2(g)}\rightleftharpoons 2HI_{(g)}$, the concentrations of ${{H}_{2}}$ , ${{I}_{2}}$ and $HI$ at equilibrium are 8.0, 3.0, and 28 moles per litre, respectively. What will be the equilibrium constant?
(A) 30.61
(B) 32.66
(C) 29.40
(D) 20.90

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 a reaction $2A\rightleftharpoons 2B+C$
The equilibrium constant is given by $K=\frac{{{[C]}^{2}}}{[A][B]}$

Complete Step by Step Answer:
The given reaction is: $H_{2(g)}+I_{2(g)}\rightleftharpoons 2HI_{(g)}$
The concentrations of reactants and products are $\left[ {{H}_{2}} \right]=8.0$ ,$\left[ {{I}_{2}} \right]=3.0$ ,$\left[ HI \right]=28$
The equilibrium constant for this reaction is given by $K=\frac{{{[HI]}^{2}}}{[{{H}_{2}}][{{I}_{2}}]}$
$K=\frac{{{(28.0)}^{2}}}{(8.0)(3.0)}$
$K=32.66$
Thus, the equilibrium constant is 32.66.
Correct Option: (B) 32.66.

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 units of equilibrium constant depend upon the number of moles of reactant and product. Its units can be given by ${{\left( mol/l \right)}^{\Delta n}}$ . Here,$\Delta n={{n}_{P}}-{{n}_{R}}=2-2=0.$ So, K has no units. To calculate the equilibrium constant, you must first understand the entire reaction and its stoichiometric coefficients. If K>1, the equilibrium favours products, and if K<1, then equilibrium favours reactants. But, if K = 1, then both reactants and products are present in the mixture in significant amounts.