Respuesta :
Answer: The value of equilibrium constant is [tex]1.39\times 10^{-4}[/tex]
Explanation:
We are given:
Percent degree of dissociation = 3.0 %
Degree of dissociation, [tex]\alpha[/tex] = 0.03
Concentration of weak acid ([HA]), c = 0.15 M
The chemical equation for the dissociation of weak acid follows:
[tex]HA\rightleftharpoons H^++A^-[/tex]
Initial: c -
At Eqllm: [tex]c-c\alpha[/tex] [tex]c\alpha[/tex] [tex]c\alpha[/tex]
So, equilibrium concentration of HA = [tex]c-c\alpha=[0.15-(0.15\times 0.03)]=0.1455M[/tex]
Equilibrium concentration of [tex][H^+]=c\alpha =[0.15\times 0.03]=0.0045M[/tex]
Equilibrium concentration of [tex][A^-]=c\alpha =[0.15\times 0.03]=0.0045M[/tex]
The expression of [tex]K_{a}[/tex] for above equation follows:
[tex]K_{a}=\frac{[H^+][A^-]}{[HA]}[/tex]
Putting values in above equation, we get:
[tex]K_{a}=\frac{0.0045\times 0.0045}{0.1455}\\\\K_{a}=1.39\times 10^{-4}[/tex]
Hence, the value of equilibrium constant is [tex]1.39\times 10^{-4}[/tex]
A weak acid is a solution that does not completely dissociate its ion in the aqueous solution. The equilibrium constant for the solution is 0.000139.
What is the equilibrium constant?
At chemical equilibrium, the value of the reaction quotient is known as the equilibrium constant. It depicts the relationship between the reactants and the product.
The ionization of a weak acid can be represented as:
[tex]\rm HA \leftrightharpoons H^{+} + A^{-}[/tex]
The initial concentration of reactant is c, and at equilibrium, it is [tex](\rm c-c\alpha)[/tex], similarly, the concentration of the products will be [tex](\rm c\alpha)[/tex]
Given,
Degree of dissociation = 0.03
The concentration of weak acid = 0.15 M
The equilibrium concentration of the reactant can be calculated as:
[tex]\begin{aligned}\rm c-c\alpha &= [0.15-(0.15\times 0.03)]\\\\&= 0.1455 \;\rm M\end{aligned}[/tex]
The equilibrium concentration of the product can be calculated as:
[tex]\begin{aligned}\rm c\alpha &= [0.15\times 0.03]\\\\&= 0.0045 \;\rm M\end{aligned}[/tex]
The dissociation constant (Ka) can be given as:
[tex]\rm K_{a} = \dfrac{[H^{+}][A^{-}]}{[HA]}[/tex]
Substituting values in the above reaction:
[tex]\begin{aligned}\rm K_{a} &= \dfrac{0.0045\times 0.0045}{0.1455}\\\\&= 1.39 \times 10^{-4} \end{aligned}[/tex]
Therefore, [tex]1.39 \times 10^{-4}[/tex] is the equilibrium constant.
Learn more about the equilibrium constant here:
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