Question

When 15 moles of ${H_2}$ and $5.2$ moles of ${I_2}$ are mixed and then allowed to attain equilibrium at $500{{\text{ }}^o}C$. At equilibrium the concentration of $HI$ is found to be $10$ moles. The equilibrium constant for the formation of $HI$ is _________.

Answer 1

$HI$ is known as hydrogen iodide prepared from hydrogen gas and molecular iodine. The hydrogen iodide is also known as hydroiodic acid and is a strong acid.

Complete step by step answer:
The reaction of hydrogen and iodine to produce $HI$ is represented as:
${H_2} + {I_2} \to 2HI$
The initial moles of the gases are $15$ and $5.2$ moles respectively. Let $x$ be the degree of dissociation of the reactants. The progress of the reaction is shown as:

| ${H_2}$ concentration| ${I_2}$ concentration| $HI$ concentration
---|---|---|---
At the beginning| $15$| $5.2$| $0$
Change in moles| $- x$ | $- x$| $2x$
At equilibrium| $15 - x$ | $5.2 - x$ | $10$

The number of moles of $HI$ at equilibrium is $10$. The value of $x$is equal to
$2x = 10$
$x = 5.$
So the degree of dissociation of the reactants is $x$. The concentrations of ${H_2}$ and ${I_2}$ at equilibrium are:
Moles of ${H_2}$ = $15 - x = 15 - 5 = 10moles$
Moles of ${I_2}$ = $5.2 - x = 5.2 - 5 = 0.2moles$
The equilibrium constant can be defined as the ratio of the products and the reactants raised to the power of the coefficients. It is represented as ${K_c}$ , and the equation is
${K_c} = \dfrac{{{{[HI]}^2}}}{{[{H_2}][{I_2}]}}$
Inserting the values of concentration of $HI$, ${H_2}$ and ${I_2}$,
${K_c} = \dfrac{{{{10}^2}}}{{10 \times 0.2}}$
${K_c} = 50$

Hence, the equilibrium constant for the formation of $HI$ is $50$.

Note:
A chemical equilibrium is a stage of a reaction which is reached when a reaction attains equilibrium between the concentrations of reactants and products. Also the rate of formation of products in the reaction is equal to the rate of formation of reactants. If the value of equilibrium constant is greater than $1$ then the equilibrium is said to favor the product bit if the value of equilibrium constant is less than $1$ then the equilibrium is said to favor reactant.