Question

One mole each of hydrogen and iodine are allowed to react at \[{{100K}}\] till the equilibrium is reached. Calculate the composition of equilibrium mixture if ${{K = 65}}{{.5}}$.

Answer 1

Hint: We have to remember the law of mass action which gives the relation between the equilibrium constant and concentrations of reactants and products. We need to use an ICE table to solve this problem. ICE table stands for Initial, Change and Equilibrium.

Complete step by step answer:
Consider the chemical reaction of hydrogen and iodine as given below:
${{{H}}_2} + {{{I}}_2} \to 2{{HI}}$
At initial concentration, number of moles of hydrogen, iodine and hydrogen iodide are given below:
$1$ , $1$ , $0$
Change in concentration required to reach equilibrium is given below:
$1 - \alpha $ , $1 - \alpha $ , $2\alpha $
We know that equilibrium constant, ${{K}} = 65.5$. This is calculated by the following formula:
${{K = }}\dfrac{{{{\left[ {{{HI}}} \right]}^2}}}{{\left[ {{{{H}}_2}} \right]\left[ {{{{I}}_2}} \right]}}$
Substituting the value of equilibrium constant, we get
\[{{65}}{{.5 = }}\dfrac{{{{\left( {2\alpha } \right)}^2}}}{{\left( {1 - \alpha } \right)\left( {1 - \alpha } \right)}}\]
On simplification, we get
\[{{65}}{{.5 = }}\dfrac{{4{\alpha ^2}}}{{1 + {\alpha ^2} - 2\alpha }}\]
\[{{65}}{{.5 + 65}}{{.5}}{\alpha ^2} - 131\alpha {{ = }}4{\alpha ^2} \Leftrightarrow {{65}}{{.5 + 61}}{{.5}}{\alpha ^2} - 131\alpha = 0\]
When we solve the above equation, we get
$\alpha = 1.33$ or $\alpha = 0.802$
We cannot use $\alpha = 1.33$ because when we use the value of $\alpha $ in $1 - \alpha $, it turns into a negative value. Thus we can use $\alpha = 0.802$.
From the value of $\alpha $, we can calculate the value of $\left[ {{{{H}}_2}} \right],\left[ {{{{I}}_2}} \right],\left[ {{{HI}}} \right]$.
i.e. $\left[ {{{{H}}_2}} \right] = \left[ {{{{I}}_2}} \right] \Leftrightarrow 1 - \alpha = 1 - 0.802 = 0.198$
And $\left[ {{{HI}}} \right] = 2\alpha \Leftrightarrow 2 \times 0.802 = 1.604$
Thus the composition of equilibrium mixture of \[\left[ {{{{H}}_2}} \right] = \left[ {{{{I}}_2}} \right] = 0.198\] and $\left[ {{{HI}}} \right] = 1.604$.

Note: When there is a state in which observable changes are not there as time goes by, such state is called equilibrium. If equilibrium constant is greater than one, then it favors products. If equilibrium constant is less than one, then it favors reactants.
We can also use partial pressures of reactants and products for calculating the equilibrium constant. This is because both concentrations and partial pressures are similarly related. When any of the reactants or products has zero, then the reaction will be shifted in that direction.