Problem 50 - Chemistry: An Atoms-Focused Approach

Question

Compounds \(A\) and \(B\) react to give a single product, \(C .\) Write the rate law for each of the following cases and determine the units of the rate constant by using the units \(M\) for concentration and s for time: a. The reaction is first order in \(A\) and second order in \(B\). b. The reaction is first order in \(A\) and second order overall. c. The reaction is independent of the concentration of \(\mathrm{A}\) and second order overall. d. The reaction is second order in both \(\mathrm{A}\) and \(\mathrm{B}\).

Step-by-Step Solution

Answer

a. The reaction is first order in A and second order in B. b. The reaction is first order in A and second order overall. c. The reaction is independent of the concentration of A and second order overall. d. The reaction is second order in both A and B.

Step 1: Write the rate law

For first order in A and second order in B, the rate law is given by: Rate = k[A][B]^2

Step 2: Determine the units of the rate constant

Let's find the units of k. The units of Rate are M/s, while the units of [A] and [B] are M. We have: [Unit of k] = (M/s) / (M)(M^2) [Unit of k] = M^{-1}s^{-1} b. The reaction is first order in A and second order overall.

Step 3: Write the rate law

For first order in A and second order overall, the rate law is given by: Rate = k[A]

Step 4: Determine the units of the rate constant

Let's find the units of k. The units of Rate are M/s, and the unit of [A] is M. [Unit of k] = (M/s) / (M) [Unit of k] = s^{-1} c. The reaction is independent of the concentration of A and second order overall.

Step 5: Write the rate law

For independent of the concentration of A and second order overall, the rate law is given by: Rate = k[B]^2

Step 6: Determine the units of the rate constant

Let's find the units of k. The units of Rate are M/s, and the unit of [B] is M. [Unit of k] = (M/s) / (M^2) [Unit of k] = M^{-1}s^{-1} d. The reaction is second order in both A and B.

Step 7: Write the rate law

For the second order in both A and B, the rate law is given by: Rate = k[A]^2[B]^2

Step 8: Determine the units of the rate constant

Let's find the units of k. The units of Rate are M/s, and the units of [A] and [B] are M. [Unit of k] = (M/s) / (M^2)(M^2) [Unit of k] = M^{-3}s^{-1}