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Chapter 11: Problem 12

A reaction has two reactants \(\mathrm{X}\) and \(\mathrm{Y}\). What is the order with respect to each reactant and the overall order of the reaction described by the following rate expressions? (a) rate \(=k_{1}[\mathrm{X}]^{2} \times[\mathrm{Y}]\) (b) rate \(=k_{2}[\mathrm{X}]\) (c) rate \(=k_{3}[\mathrm{X}]^{2} \times[\mathrm{Y}]^{2}\) (d) rate \(=k_{4}\)

Short Answer

Expert verified
Question: Determine the order with respect to each reactant and the overall order of the reaction for the following rate expressions: a) rate \(=k_{1}[\mathrm{X}]^{2} \times[\mathrm{Y}]\) b) rate \(=k_{2}[\mathrm{X}]\) c) rate \(=k_{3}[\mathrm{X}]^{2} \times[\mathrm{Y}]^{2}\) d) rate \(=k_{4}\) Answer: a) Order with respect to X: 2, Order with respect to Y: 1, Overall order: 3. b) Order with respect to X: 1, Order with respect to Y: 0, Overall order: 1. c) Order with respect to X: 2, Order with respect to Y: 2, Overall order: 4. d) Order with respect to X: 0, Order with respect to Y: 0, Overall order: 0.

Step by step solution

01

a) Determine the order for X and Y in the first rate expression

For the rate expression rate \(=k_{1}[\mathrm{X}]^{2} \times[\mathrm{Y}]\), we can see that the concentration of X is raised to the power of 2, while the concentration of Y is raised to the power of 1. Thus, the order with respect to X is 2, and the order with respect to Y is 1.
02

a) Determine the overall order of the reaction for the first rate expression

To determine the overall order of the reaction, we sum the orders of each reactant. In this case, that is \(2(\text{for X}) + 1(\text{for Y})\). So, the overall order of the reaction is 3.
03

b) Determine the order for X in the second rate expression

For the rate expression rate \(=k_{2}[\mathrm{X}]\), the concentration of X is raised to the power of 1, and there is no dependence on the concentration of Y. Thus, the order with respect to X is 1, and the order with respect to Y is 0.
04

b) Determine the overall order of the reaction for the second rate expression

The overall order of the reaction is the sum of the orders of each reactant, which is \(1(\text{for X}) + 0(\text{for Y})\). Therefore, the overall order of the reaction is 1.
05

c) Determine the order for X and Y in the third rate expression

For the rate expression rate \(=k_{3}[\mathrm{X}]^{2} \times[\mathrm{Y}]^{2}\), the concentration of X is raised to the power of 2, and the concentration of Y is raised to the power of 2 as well. Thus, the order with respect to X is 2, and the order with respect to Y is 2.
06

c) Determine the overall order of the reaction for the third rate expression

To determine the overall order of the reaction, we sum the orders of each reactant, which is \(2(\text{for X}) + 2(\text{for Y})\). Thus, the overall order of the reaction is 4.
07

d) Determine the order and overall order for the fourth rate expression

For the rate expression rate \(=k_{4}\), there is no dependence on the concentration of X or Y. Thus, the order with respect to X is 0, and the order with respect to Y is 0.
08

d) Calculate the overall order of the reaction for the fourth rate expression

The overall order of the reaction is the sum of the orders of each reactant, which is \(0(\text{for X}) + 0(\text{for Y})\). Therefore, the overall order of the reaction is 0.

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Most popular questions from this chapter

Sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) hydrolyzes into glucose and fructose. The hydrolysis is a first-order reaction. The half-life for the hydrolysis of sucrose is \(64.2\) min at \(25^{\circ} \mathrm{C}\). How many grams of sucrose in \(1.25 \mathrm{~L}\) of a \(0.389 \mathrm{M}\) solution are hydrolyzed in \(1.73\) hours?

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