Problem 48 - Chemistry: An Atoms-Focused Approach

Question

Determine the overall order of the following rate laws and the order with respect to each reactant. a. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}]^{1 / 2}\) b. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}][\mathrm{C}]\) c. Rate \(=k[\mathrm{A}][\mathrm{B}]^{3}[\mathrm{C}]^{1 / 2}\)

Step-by-Step Solution

Answer

Question: Determine the order of each reaction with respect to each reactant and the overall order of the reactions given below: a. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}]^{1 / 2}\) b. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}][\mathrm{C}]\) c. Rate \(=k[\mathrm{A}][\mathrm{B}]^{3}[\mathrm{C}]^{1 / 2}\) Answer: a. Order with respect to A: 2 Order with respect to B: 1/2 Overall order of the reaction: 2.5 b. Order with respect to A: 2 Order with respect to B: 1 Order with respect to C: 1 Overall order of the reaction: 4 c. Order with respect to A: 1 Order with respect to B: 3 Order with respect to C: 1/2 Overall order of the reaction: 4.5

Step 1: Order with respect to A

In this rate law, the exponent of A is '2'. Therefore, the order of the reaction with respect to A is 2.

Step 2: Order with respect to B

In the same rate law, the exponent of B is '1/2'. Hence, the order of the reaction with respect to B is 1/2.

Step 3: Overall order of the reaction

The overall order of the reaction is the sum of orders with respect to each reactant, which is 2 + 1/2 = 5/2 or 2.5. b. Rate \(=k[\mathrm{A}]^{2}[\mathrm{B}][\mathrm{C}]\)

Step 4: Order with respect to A

The exponent of A in this rate law is '2', so the order with respect to A is 2.

Step 5: Order with respect to B

The exponent of B in this rate law is '1', so the order with respect to B is 1.

Step 6: Order with respect to C

The exponent of C in this rate law is '1', so the order with respect to C is 1.

Step 7: Overall order of the reaction

The overall order of the reaction is the sum of individual orders: 2 + 1 + 1 = 4. c. Rate \(=k[\mathrm{A}][\mathrm{B}]^{3}[\mathrm{C}]^{1 / 2}\)

Step 8: Order with respect to A

The exponent of A in this rate law is '1', so the order with respect to A is 1.

Step 9: Order with respect to B

The exponent of B in this rate law is '3', so the order with respect to B is 3.

Step 10: Order with respect to C

The exponent of C in this rate law is '1/2', so the order with respect to C is 1/2.

Step 11: Overall order of the reaction

The overall order of the reaction is the sum of individual orders: 1 + 3 + 1/2 = 9/2 or 4.5.