Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (e) By what factor does the rate change when the concentrations of all three reactants are tripled?

Verified step by step guidance

1. Step 1: Understand the rate law for the reaction. The rate law for a reaction is an equation that shows how the rate of a reaction depends on the concentrations of the reactants. In this case, the rate law is given by Rate = k[A][B]^0[C]^2, where k is the rate constant, [A], [B], and [C] are the concentrations of the reactants A, B, and C, respectively.
2. Step 2: Understand the order of reaction. The order of a reaction with respect to a particular reactant is the power to which its concentration in the rate equation is raised. In this case, the reaction is first order in A, zero order in B, and second order in C.
3. Step 3: Calculate the new rate when the concentrations of all three reactants are tripled. According to the rate law, if the concentration of A is tripled, the rate will triple because the reaction is first order in A. If the concentration of B is tripled, the rate will not change because the reaction is zero order in B. If the concentration of C is tripled, the rate will increase by a factor of 3^2 = 9 because the reaction is second order in C.
4. Step 4: Multiply the changes in the rate due to each reactant to find the total change in the rate. In this case, the total change in the rate is 3 (from A) * 1 (from B) * 9 (from C) = 27.
5. Step 5: Therefore, when the concentrations of all three reactants are tripled, the rate of the reaction increases by a factor of 27.

Key Concepts

Rate Law

The rate law of a reaction expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is determined by the reaction order with respect to each reactant, which indicates how the rate is affected by changes in concentration. For example, a first-order reaction in a reactant means that doubling its concentration will double the reaction rate.

Reaction Order

Reaction order refers to the exponent to which the concentration of a reactant is raised in the rate law. It can be zero, first, second, or higher, indicating how the rate of reaction changes with varying concentrations. In the given reaction, A is first order, B is zero order, and C is second order, meaning that only the concentrations of A and C will affect the rate when their concentrations change.

Effect of Concentration Changes

When the concentrations of reactants are changed, the overall rate of the reaction can be calculated by substituting the new concentrations into the rate law. For the given reaction, if the concentrations of A, B, and C are all tripled, the rate will change according to the orders: the rate will increase by a factor of 3 (for A) and 9 (for C), while B remains unchanged, leading to a total factor of 27 for the rate change.