Question

If degree of dissociation is \[0.5\] at equilibrium, then the equilibrium constant \[{K_c}\] for the given reaction is

Answer 1

Hint: The degree of dissociation of any compound or molecule is the dissociation of the reactants from its concentration. For weak acids it is less than 1.

Complete step by step answer:
The degree of dissociation is represented as \[\alpha \]and is the dissociation of the hydrogen iodide. the equilibrium constant \[{K_c}\]is measured at equilibrium by the ratio of the concentration of the product to the reactant concentration.
Suppose the concentration of hydrogen iodide is \[C\,\]

As we know, the equilibrium constant \[{K_c}\]is,
\[{K_c} = \dfrac{{\left[ {{H_2}} \right]\left[ {{I_2}} \right]}}{{{{\left[ {HI} \right]}^2}}}\]
Now, By putting the values of concentration of reactants and products of above equation in the \[{K_c}\]we can easily get the value of \[{K_c}\] as
\[\begin{array}{l}
{K_c} = \dfrac{{\left[ {C\alpha } \right]\left[ {C\alpha } \right]}}{{{{\left[ {C - C\alpha } \right]}^2}}}\\
{K_c} = \dfrac{{\alpha x\alpha }}{{{{\left( {1 - \alpha } \right)}^2}}}\\
{K_c} = \dfrac{{0.5x0.5}}{{{{0.5}^2}}} = 1
\end{array}\]

Note:
The equilibrium constant also helps to find the direction of the reaction whether the reaction will proceed to the right direction or left direction or will remain at the equilibrium.
For this purpose, we calculate the reaction quotient\[Q\].the reaction quotient is the ratio of the concentration of the product to that of the reactant concentration.
If \[{Q_c}\]( the reaction quotient with molar concentrations)> \[{K_c}\], the reaction will proceed from right to left direction (backward direction).
If \[{Q_c}\]( the reaction quotient with molar concentrations <\[{K_c}\], the reaction will proceed to from left to right direction (forward direction).
If \[{Q_c}\]\[ = \]\[{K_c}\],the reaction mixture is already at equilibrium and no reaction occurs.