Question Video: Determining the Equation for 𝐾𝑐 from a General Reaction Chemistry • Third Year of Secondary School

Video Transcript

Consider the general reaction shown. aA plus bB are in equilibrium with cC plus dD. What is the expression for the equilibrium constant for this general reaction? Take capital A in brackets and capital B in brackets to be the molar concentrations of the reactants, capital C in brackets and capital D in brackets to be the molar concentrations of the products, and lowercase a, b, c, and d to be the stoichiometric coefficients in the balanced equation.

In the given reaction equation, the lowercase letters represent stoichiometric coefficients, and the uppercase letters represent chemical formulas. We can tell from the equilibrium arrow that this reaction is an equilibrium reaction. Equilibrium reactions carried out in a closed system can reach dynamic equilibrium. Dynamic equilibrium is an equilibrium between forward and reverse reactions, where both reactions occur at the same nonzero rate and the concentrations of the reactants and products remain constant.

When dynamic equilibrium is established and the concentrations of the reactants and products no longer change, we can use these concentrations to quantify the equilibrium. To quantify an equilibrium using concentrations, we can use the equilibrium constant for concentration represented by 𝐾 𝑐. The equilibrium constant for concentration expresses the ratio between the equilibrium concentrations of the reactants and products. In its simplest form, the equilibrium constant for concentration can be written as 𝐾 𝑐 equals the concentration of the products divided by the concentration of the reactants.

To answer this question, we need to construct an expression for the equilibrium constant for the general reaction. We know from the simple 𝐾 𝑐 expression that the concentrations of the products should be in the numerator and the concentrations of the reactants should be in the denominator. So, we should write capital C and D inside brackets in the numerator and capital A and B inside brackets in the denominator.

To complete an equilibrium constant for concentration expression, we need to consider the stoichiometry. Lowercase a, b, c, and d represent the stoichiometric coefficients in the balanced equation. Stoichiometric coefficients are included in the equilibrium constant expression as exponents following the respective molar concentration. This completes the expression for the equilibrium constant for the general reaction.

𝐾 𝑐 equals the concentration of C raised to c times the concentration of D raised to d divided by the concentration of A raised to a times the concentration of B raised to b.