Question

$ HI $ was heated in a sealed tube at $ {440^ \circ }C $ till the equilibrium is reached. $ HI $ was found to be $ 22% $ decomposed The equilibrium constant for the dissociation of $ HI $ is : [ $ 2HI \rightleftharpoons {H_2} + {I_2} $ ]
A. $ 0.282 $
B. $ 0.0796 $
C. $ 0.0199 $
D. $ 1.99 $

Answer 1

Hint: Chemical equilibrium is the state of a system in which the concentration of the reactant and the concentration of the products do not change over time and the system's characteristics do not change. The equilibrium constant can be described as the ratio between the amount of reactant and the amount of product used to determine chemical behaviour in a chemical reaction.

Complete answer:
When $ HI $ is heated at equilibrium, the following reaction takes place
 $ 2HI \rightleftharpoons {H_2} + {I_2} $

$ 2x $	$ 0 $	$ 0 $
$ 2-2x $	$ x $	$ x $

At initial concentration, there are $ 2 $ moles of $ HI $ and $ 0 $ moles of $ {H_2} $ and $ {I_2} $ .
At equilibrium, moles of $ HI $ become $ 2 - 2x $ and $ x $ for $ {H_2} $ and $ {I_2} $ .
We know that $ 22% $ is decomposed. So $ x = 0.22 $
So, equilibrium constant will be,
 $ {K_c} = \dfrac{{x \times x}}{{{{(2 - 2x)}^2}}} $
 $ {K_c} = \dfrac{{0.22 \times 0.22}}{{{{(2 - 2 \times 0.22)}^2}}} $
 $ {K_c} = \dfrac{{0.0484}}{{{{(2 - 0.44)}^2}}} $
 $ {K_c} = \dfrac{{0.0484}}{{2.4533}} $
 $ {K_c} = 0.0199 $
The equilibrium constant for the dissociation of $ HI $ is $ 0.0199 $ .
Hence, the correct option is C. $ 0.0199 $ .

Additional Information:
The equilibrium constant ( $ {K_c} $ ) can be used to predict the magnitude of a reaction, or how quickly the reactants disappear. The value of the equilibrium constant indicates the number of reactants and products present.
The direction of the reaction can be predicted using the equilibrium constant. The reaction quotient is a term that is similar to the equilibrium constant except that the conditions are not at equilibrium.

Note:
The following are some of the factors that influence the equilibrium constant: Any changes in the product or reactant's concentration. Changes in the system's pressure. When the system's temperature has shifted. Inert gas is being added. Adding catalyst to the reaction.