Problem 47 - Chemistry: An Atoms-Focused Approach

Question

For each of the following rate laws, determine the order with respect to each reactant and the overall reaction order. a. Rate \(=k[\mathrm{A}][\mathrm{B}]\) b. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}]\) c. Rate \(=k[\mathrm{A}][\mathrm{B}]^{3}\)

Step-by-Step Solution

Answer

Question: Determine the reaction order with respect to each reactant and the overall reaction order for the following rate laws: a. Rate \(= k[\mathrm{A}][\mathrm{B}]\) b. Rate \(= k[\mathrm{A}]^{2}[\mathrm{B}]\) c. Rate \(= k[\mathrm{A}][\mathrm{B}]^{3}\) Answer: a. The reaction is first order with respect to A and first order with respect to B. The overall reaction order is 2. b. The reaction is second order with respect to A and first order with respect to B. The overall reaction order is 3. c. The reaction is first order with respect to A and third order with respect to B. The overall reaction order is 4.

Step 1: Finding orders related to reactants

The rate law is given as Rate \(= k[\mathrm{A}][\mathrm{B}]\). This means that the reaction is first order with respect to A and first order with respect to B, since the exponents of the concentrations are both equal to 1.

Step 2: Finding overall reaction order

To find the overall reaction order, we add the individual orders with respect to each reactant: \(1 + 1 = 2\). Thus, the overall reaction order is 2. b. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}]\)

Step 3: Finding orders related to reactants

The rate law is given as Rate \(= k[\mathrm{A}]^{2}[\mathrm{B}]\). This means that the reaction is second order with respect to A and first order with respect to B, as shown by the exponents of the concentrations.

Step 4: Finding overall reaction order

To find the overall reaction order, we add the individual orders with respect to each reactant: \(2 + 1 = 3\). Thus, the overall reaction order is 3. c. Rate \(=k[\mathrm{A}][\mathrm{B}]^{3}\)

Step 5: Finding orders related to reactants

The rate law is given as Rate \(= k[\mathrm{A}][\mathrm{B}]^{3}\). This means that the reaction is first order with respect to A and third order with respect to B, as shown by the exponents of the concentrations.

Step 6: Finding overall reaction order

To find the overall reaction order, we add the individual orders with respect to each reactant: \(1 + 3 = 4\). Thus, the overall reaction order is 4.