Multiple Choice
Using the figure, calculate the value of the rate constant, k, for the reaction. Express your answer using two significant figures.
15. Chemical Kinetics
Rate Law
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What is the rate law for the following mechanism in terms of the overall rate constant k?Step 1: A + B → C (fast)Step 2: C → D (slow)Express your answer in terms of k and the necessary concentrations (e.g., k*[A]^3*[D]).
A
k*[A]^2*[B]
B
k*[C]
C
k*[A]*[B]
D
k*[B]
Verified step by step guidance1
Identify the slow step in the mechanism, as it determines the rate law for the overall reaction. In this case, Step 2: C → D is the slow step.
Write the rate law for the slow step. Since Step 2 is the slow step, the rate law is based on the concentration of C: rate = k'[C], where k' is the rate constant for the slow step.
Recognize that the intermediate C is not part of the overall reaction, so we need to express [C] in terms of the reactants A and B.
Use the fast equilibrium assumption for Step 1: A + B ⇌ C. The rate of formation of C is equal to the rate of its consumption in the fast step, so k1[A][B] = k-1[C], where k1 and k-1 are the rate constants for the forward and reverse reactions of Step 1.
Solve for [C] in terms of [A] and [B]: [C] = (k1/k-1)[A][B]. Substitute this expression into the rate law for the slow step to get the overall rate law: rate = k*[A][B], where k = k'*(k1/k-1).
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