Final answer:
The best representation for the equilibrium constant K, where a balanced chemical equation's coefficients are squared, is ( [a] * [b] )^2 / ( [x] * [y] )^2, which properly reflects the squared concentrations of the products over the reactants according to the rule that exponents of K are multiplied by the constant the equation is multiplied by.
Step-by-step explanation:
To determine the best representation for the equilibrium constant (K), we need to examine the chemical equilibrium expression for a balanced reaction. For a reaction aA + bB ⇌ cC + dD, the equilibrium constant expression is K = ([C]^c * [D]^d) / ([A]^a * [B]^b). Coefficients a, b, c, and d become exponents. If our balanced chemical equation is multiplied by a constant, the exponents of K will be multiplied by that constant as well.
Suppose our equation is A + B ⇌ X + Y and is then balanced. If it is multiplied by 2 to get 2A + 2B ⇌ 2X + 2Y, according to the information provided, the new equilibrium constant, K", would be (K')^(1/2). Applying this logic, if the chemical equation's coefficients are squared, the exponents in the equilibrium constant expression are also squared, leading to K" = (K^1)^(1/2) = √√K'.
Therefore, the correct representation for K, considering the squared concentrations, would be answer choice B: ( [a] * [b] )^2 / ( [x] * [y] )^2, which represents the products squared in the numerator and the reactants squared in the denominator. This appropriately reflects the squared coefficients when the balanced equation is multiplied by 2.