Rate expression fo NH3 synthesis is

Explanation

Kc: This represents the equilibrium constant for the reaction, not the rate expression itself. However, the equilibrium constant is related to the rate constants of the forward and reverse reactions, so it's often used in conjunction with rate expressions.X^2: This term signifies the concentration of NH3 at equilibrium, raised to the power of its stoichiometric coefficient (2) in the balanced equation.(a - x) and (b - x): These terms represent the equilibrium concentrations of the reactants, N2 and H2, respectively. They are expressed as initial concentrations (a and b) minus the amount that has reacted to form NH3 (x).Key reasons for eliminating other options:Options b and c: They include a volume term (v), which is not present in the actual rate expression for NH3 synthesis. The rate expression relates concentrations, not volume.Option d: It has complicated terms like 4X^2v^2 and (b - 3x)^3, which are not consistent with the stoichiometry of the reaction.toichiometry and Rate Expression:The balanced equation for NH3 synthesis is:2(g) + 3H2(g) ⇌ 2NH3(g)The rate expression is derived based on the reaction's stoichiometry and the law of mass action:Rate = k[N2][H2]^3At equilibrium, the rate of the forward and reverse reactions are equal, and the equilibrium constant (Kc) is expressed as:Kc = [NH3]^2 / ([N2][H2]^3)Substituting the equilibrium concentrations in terms of a, b, and x, we get the correct rate expression:Kc = X^2 / (a - x)(b - x)