chemistry homework question

Question

consider the mechanism

Step 1: A --> B+C equilibrium

Step 2: C + D---> E slow

Overall: A+D--> B+E

Determine the rate law for the overall reaction, where the overall rate constant is represented as 𝑘.

can someone show me the steps to this.

Answer 1

Since the slow step is NOT the first step, we can't just use it, but must incorporate the first step (equilibrium) into our calculations.

Step 1: A <==> B + C (let k1 = rate constant forward and k2 = rate constant reverse)

k1[A] = k2[B][C] and since C is an intermediate and appears in the slow step (step 2), we will solve for [C] and replace it because an intermediate cannot appear in the overall rate law...

[C] = k1/k2[A]/[B] now we can use this in step 2.

Step 2: C + D ==> E

Rate = k3[C][D] since it is the slow step.

Plugging in our expression for [C] determined above, we have..

rate = k3k1/k2 [A][D]/[B] and as B is a product, it can't be in the rate law.

Combining rate constants k1, k2 and k3 and calling it k, we have...

Rate = k[A][D] which is in agreement with the overall equation of A + D => B + E