In a reversible reaction, two substances are in equilibrium. If the co...
Explanation:
When a reversible reaction is at equilibrium, the concentrations of the reactants and products remain constant. The equilibrium constant (K) is a numerical value that represents the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium.
In this case, let's consider a reversible reaction represented as:
A + B ⇌ C + D
Where A and B are reactants and C and D are products.
Now, if the concentration of each substance is reduced to half, we can denote the new concentrations as:
[A] = [A]₀/2
[B] = [B]₀/2
[C] = [C]₀/2
[D] = [D]₀/2
The equilibrium constant (K) is defined as:
K = ([C] * [D]) / ([A] * [B])
Substituting the new concentrations into the equilibrium constant expression, we get:
K' = ([C]₀/2 * [D]₀/2) / ([A]₀/2 * [B]₀/2)
Simplifying the expression, we have:
K' = ([C]₀ * [D]₀) / ([A]₀ * [B]₀) * (1/2 * 1/2)
K' = K * (1/4)
Therefore, the equilibrium constant (K') is reduced to one-fourth (1/4) of its original value (K). Hence, the correct answer is option 'D', i.e., "reduced to one-fourth its original value".
It's important to note that the equilibrium constant depends only on the stoichiometry of the reaction and the temperature, but not on the initial concentrations of the reactants and products. Therefore, reducing the concentration of each substance to half does not change the equilibrium constant value.