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Question: If degree of dissociation is \(0.5\) at equilibrium, then the equilibrium constant \(K_c\) for the g...

If degree of dissociation is 0.50.5 at equilibrium, then the equilibrium constant KcK_c for the given reaction is 2HI⇌H2+I22HI \rightleftharpoons {H_2} + {I_2}
A. 0.5{\mathbf{0}}.{\mathbf{5}}
B. 0.25{\mathbf{0}}.{\mathbf{25}}
C. 1    {\mathbf{1}}\;\;
D. 4{\mathbf{4}}

Explanation

Solution

in this question we have to find out the equilibrium constant for the given reaction of hydrogen and iodine by using the equilibrium constant formula.

Formula used:
Equilibrium Constant,Kc=[C][D][A][B]=Π(PRODUCT)Product CoefficientΠ(REACTANT)Reactant CoefficientK_c = \dfrac{{{{\left[ C \right]}}{{\left[ D \right]}}}}{{[A][B]}}=\dfrac{{\Pi(PRODUCT)}^{Product \, Coefficient}}{{\Pi(REACTANT)}^{Reactant\, Coefficient}}

Complete step by step answer
Equilibrium constant is related to forward and backward rate constants of the reaction involved in reaching the state of equilibrium. It is determined by free energy for the whole system at constant temperature and pressure.
While determining the value of equilibrium constant KcK_c, concentration is expressed in mol inverse 1
By putting values in formula, we get,
Kc=[H2][I2]    [2HI]2    =[0.5]2[0.5]2=1K_c = \dfrac{{{{\left[ {{H_2}} \right]}}\left[ {{I_2}} \right]\;\;}}{{{{\left[ {2HI} \right]}^{2\;\;}}}} = \dfrac{{{{\left[ {0.5} \right]}^2}}}{{{{\left[ {0.5} \right]}^2}}} = 1

**Hence equilibrium constant KcK_c of given reaction is option C that is 11.

Additional information:**
One must have a prior knowledge of equilibrium constants, because it is most important for understanding many biochemical and chemical systems. The process of transport of oxygen in blood by hemoglobin is known for its biochemical process. It is also known as acid-base homeostasis.

Note:
The equilibrium constant is a ratio between the concentrations of the products to the concentration of the reactants. In a chemical reaction the equilibrium constant is the value of its reaction quotient at chemical equilibrium, which shows that the reaction has reached a state where there is no measurable tendency towards further change in it. The concentration in an equilibrium mixture are related by equilibrium equation Kc=[C][D][A][B]K_c = \dfrac{{[C][D]}}{{[A][B]}} where KcK_c is equilibrium constant and the expression on right side is called the equilibrium constant expression.