Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 11

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

Short Answer

Expert verified
Question: Determine the order of the reaction with respect to each reactant (A and B) as well as the overall order for the following rate expressions: a) rate=k1[A]^3 b) rate=k2[A][B] c) rate=k3[A][B]^2 d) rate=k4[B] Answer: a) Order with respect to A: 3, Order with respect to B: 0, Overall order: 3 b) Order with respect to A: 1, Order with respect to B: 1, Overall order: 2 c) Order with respect to A: 1, Order with respect to B: 2, Overall order: 3 d) Order with respect to A: 0, Order with respect to B: 1, Overall order: 1

Step by step solution

01

(a) Reaction order from rate=k1[A]^3

In this case, the rate expression is given by rate \(= k_{1}[\mathrm{~A}]^{3}\). Since the concentration of reactant A is raised to the power of 3, the order of the reaction with respect to A is 3. B is not present in this rate expression, so the order with respect to B is 0. Adding the orders of each reactant together, the overall order of this reaction is 3.
02

(b) Reaction order from rate=k2[A][B]

In this case, the rate expression is given by rate \(=k_{2}[\mathrm{~A}] \times [\mathrm{B}]\). The order of the reaction with respect to A is 1, as the concentration of A is raised to the power of 1. Similarly, the order with respect to B is also 1. Adding the orders together, the overall order of this reaction is 2.
03

(c) Reaction order from rate=k3[A][B]^2

In this case, the rate expression is given by rate \(=k_{3}[\mathrm{~A}] \times [\mathrm{B}]^{2}\). The order with respect to A is 1, as the concentration of A is raised to the power of 1. The order with respect to B is 2 since the concentration of B is raised to the power of 2. Adding the orders together, the overall order of this reaction is 3.
04

(d) Reaction order from rate=k4[B]

In this case, the rate expression is given by rate \(=k_{4}[\mathrm{~B}]\). Since the concentration of reactant B is raised to the power of 1, the order of the reaction with respect to B is 1. A is not present in this rate expression, so the order with respect to A is 0. Adding the orders of each reactant together, the overall order of this reaction is 1.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Diethylhydrazine reacts with iodine according to the following equation: $$\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}(l)+\mathrm{I}_{2}(a q) \longrightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{~N}_{2}(l)+2 \mathrm{HI}(a q)$$ The rate of the reaction is followed by monitoring the disappearance of the purple color due to iodine. The following data are obtained at a certain temperature. $$ \begin{array}{cccc} \hline \text { Expt. } & {\left[\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}\right]} & {\left[\mathrm{I}_{2}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{h}) \\ \hline 1 & 0.150 & 0.250 & 1.08 \times 10^{-4} \\ 2 & 0.150 & 0.3620 & 1.56 \times 10^{-4} \\ 3 & 0.200 & 0.400 & 2.30 \times 10^{-4} \\ 4 & 0.300 & 0.400 & 3.44 \times 10^{-4} \\ \hline\end{array}$$ (a) What is the order of the reaction with respect to diethylhydrazine, iodine, and overall? (b) Write the rate expression for the reaction. (c) Calculate \(k\) for the reaction. (d) What must \(\left[\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}\right]\) be so that the rate of the reaction is \(5.00 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{h}\) when \(\left[\mathrm{I}_{2}\right]=0.500 ?\)

Hypofluorous acid, HOF, is extremely unstable at room temperature. The following data apply to the decomposition of HOF to \(\mathrm{HF}\) and \(\mathrm{O}_{2}\) gases at a certain temperature. $$\begin{array}{cl}\hline \text { Time (min) } & \text { [HOF] } \\\\\hline 1.00 & 0.607 \\\2.00 & 0.223 \\\3.00 & 0.0821 \\\4.00 & 0.0302 \\\5.00 & 0.0111 \\\\\hline \end{array}$$ (a) By plotting the data, show that the reaction is first-order. (b) From the graph, determine \(k\). (c) Using \(k\), find the time it takes to decrease the concentration to \(0.100 \mathrm{M}\) (d) Calculate the rate of the reaction when [HOF] \(=0.0500 M\).

Express the rate of the reaction $$2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$ in terms of (a) \(\Delta\left[\mathrm{C}_{2} \mathrm{H}_{6}\right]\) (b) \(\Delta\left[\mathrm{CO}_{2}\right]\)

Nitrosyl bromide (NOBr) decomposes to nitrogen oxide and bromine. Use the following data to determine the order of the decomposition reaction of nitrosyl bromide. $$\begin{array}{cccccc}\hline \text { Time (s) } & 0 & 6 & 12 & 18 & 24 \\ \text { [NOBr] } & 0.0286 & 0.0253 & 0.0229 & 0.0208 & 0.0190 \\\\\hline\end{array}$$

A sample of sodium-24 chloride contains \(0.050 \mathrm{mg}\) of \(\mathrm{Na}-24\) to study the sodium balance of an animal. After \(24.9 \mathrm{~h}, 0.016 \mathrm{mg}\) of \(\mathrm{Na}-24\) is left. What is the half- life of \(\mathrm{Na}-24 ?\)
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

Making Measurements

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Analysis

Read Explanation

Organic Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free