For a general equation of the nature xP + yQ → mR + nS, the expression for the equilibrium constant is

Analysis

The question asks for the mathematical expression of the equilibrium constant ($K_c$) for a reversible chemical reaction. In chemistry, the equilibrium constant is defined by the Law of Mass Action.

Concept: The Law of Mass Action

The Law of Mass Action states that for a reversible reaction at equilibrium, the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants—each raised to the power of their respective stoichiometric coefficients—is constant at a given temperature.

For the general reaction:

The equilibrium constant ($K_c$) is expressed as:

Step-by-Step Solution

1. Identify the products: In the equation $xP + yQ \rightarrow mR + nS$, the products are R and S.
2. Identify the reactants: The reactants are P and Q.
3. Apply the coefficients as powers: • The concentration of R is raised to the power of its coefficient, $m$ $\rightarrow [R]^m$ • The concentration of S is raised to the power of its coefficient, $n$ $\rightarrow [S]^n$ • The concentration of P is raised to the power of its coefficient, $x$ $\rightarrow [P]^x$ • The concentration of Q is raised to the power of its coefficient, $y$ $\rightarrow [Q]^y$
4. Construct the fraction: Place the product of the products in the numerator and the product of the reactants in the denominator: $$K_c = \frac{[R]^m [S]^n}{[P]^x [Q]^y}$$

Conclusion

Comparing this result to the given options, we see that it matches option C.

Exam Tip: Always remember the phrase "Products over Reactants" (P/R). A common mistake students make is flipping the fraction or multiplying the coefficients instead of using them as exponents. Ensure your coefficients are written as superscripts, not as multipliers in front of the brackets!