Question

Write the rate law for the reaction in which the order with respect to the reactants X, Y and Z are 1/2, 3/2 and zero respectively.

Hint:

An order of zero means that the rate of the reaction is completely independent of the concentration of that specific reactant. Changing [Z] will have no effect on how fast the reaction goes.

Answer 1

Concept: The Rate Law is an expression that relates the rate of a chemical reaction to the molar concentration of its reactants. In a general reaction, the rate is proportional to the concentration of each reactant raised to a power, which is known as the order of the reaction with respect to that reactant.
For a reaction involving reactants X, Y, and Z, the general rate law is: Rate = k[X]ᵃ[Y]ᵇ[Z]ᶜ Where: • k is the rate constant. • a, b, and c are the orders of the reaction with respect to X, Y, and Z respectively.
Given values for the orders: • Order with respect to X (a) = 1/2 • Order with respect to Y (b) = 3/2 • Order with respect to Z (c) = 0
Substituting these into the general expression: Rate = k[X]¹/²[Y]³/²[Z]⁰
Since any value raised to the power of zero is equal to 1 ([Z]⁰ = 1), the simplified rate law is: Rate = k[X]¹/²[Y]³/²