/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 A reaction has two reactants \(\... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rate Law
In chemical kinetics, the rate law is a mathematical expression that links the rate of a chemical reaction to the concentration of its reactants. It is always crucial to understand the rate law because it helps in determining how changes in concentration affect the speed of the reaction.
For a given reaction with two reactants, A and B, the rate law can be expressed as follows:
  • rate = k × [A]^x
  • [B]^y
The terms in the brackets represent the concentrations of reactants, and the exponents (x and y) represent the reaction orders with respect to each reactant. The rate constant, denoted by "k," is a factor that incorporates the effects of temperature and other environmental conditions to the reaction speed.
Each exponent in the rate law indicates how sensitive the reaction rate is to the concentration of each reactant. The sum of these exponents gives the overall reaction order. Understanding the rate law is fundamental for predicting how fast a reaction proceeds and for deriving potential methods to control the reaction.
Chemical Kinetics
Chemical kinetics is the branch of chemistry that concerns itself with the speed, or rate, at which chemical reactions occur. It connects the path of reaction, known as the reaction mechanism, with the rate at which transformations happen. This field is fundamental for predicting and controlling how fast a chemical process should complete. Key factors influencing reaction rates include:
  • Concentration: As concentration increases, the number of collisions between reactant molecules also increases, generally speeding up the reaction.
  • Temperature: Higher temperatures usually result in faster reactions because molecules move more energetically.
  • Catalysts: These substances lower the activation energy needed, significantly increasing the rate of reaction without being consumed themselves.
Understanding chemical kinetics allows scientists and engineers to design more efficient chemical processes and reactors. It equips them with the insights necessary to optimize conditions for favorable product yields and energy consumption.
Reaction Mechanisms
A reaction mechanism describes how reactants transform into products through a series of elementary steps. Each of these steps represents a simple reaction that contributes to the overall reaction process. Recognizing the reaction mechanism provides insights into the molecular changes occurring during the reaction pathway. Mechanisms are determined through experimental data combined with theoretical models. Key points in understanding mechanisms include:
  • Intermediates: These are transient species that are formed and consumed during the mechanism.
  • Rate-determining step: This is the slowest step in the process and it controls the overall rate of the reaction.
  • Stoichiometric coefficients: These play a crucial role in establishing the connection between elementary steps and the observed reaction rate law.
By understanding the mechanism of a reaction, chemists can often predict the conditions under which a reaction will occur most promptly and efficiently, and potentially identify any side reactions that may interfere with the desired product formation.

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

The decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) to \(\mathrm{NO}_{2}\) and \(\mathrm{NO}_{3}\) is a first-order gas-phase reaction. At \(25^{\circ} \mathrm{C}\), the reaction has a half-life of \(2.81\) s. At \(45^{\circ} \mathrm{C}\), the reaction has a half-life of \(0.313 \mathrm{~s}\). What is the activation energy of the reaction?

WEB When boron trifluoride reacts with ammonia, the following \(T\) reaction occurs: for $$\mathrm{BF}_{3}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{BF}_{3} \mathrm{NH}_{3}(g)$$ The following data are obtained at a particular temperature: $$\begin{array}{cccc}\hline \text { Expt. } & {\left[\mathrm{BF}_{3}\right]} & {\left[\mathrm{NH}_{3}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}) \\\\\hline 1 & 0.100 & 0.100 & 0.0341 \\ 2 & 0.200 & 0.233 & 0.159 \\ 3 & 0.200 & 0.0750 & 0.0512 \\ 4 & 0.300 & 0.100 & 0.102 \\\\\hline\end{array}$$

The equation for the iodination of acetone in acidic solution is $$\mathrm{CH}_{3} \mathrm{COCH}_{3}(a q)+\mathrm{I}_{2}(a q) \longrightarrow \mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{I}(a q)+\mathrm{H}^{+}(a q)+\mathrm{I}^{-}(a q)$$ The rate of the reaction is found to be dependent not only on the concentration of the reactants but also on the hydrogen ion concentration. Hence the rate expression of this reaction is $$\text { rate }=k\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]^{m}\left[\mathrm{I}_{2}\right]^{n}\left[\mathrm{H}^{+}\right]^{p}$$ The rate is obtained by following the disappearance of iodine using starch as an indicator. The following data are obtained: $$ \begin{array}{cccc} \hline\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right] & \left.\mathrm{[H}^{+}\right] & {\left[\mathrm{I}_{2}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}) \\ \hline 0.80 & 0.20 & 0.001 & 4.2 \times 10^{-6} \\ 1.6 & 0.20 & 0.001 & 8.2 \times 10^{-6} \\ 0.80 & 0.40 & 0.001 & 8.7 \times 10^{-6} \\ 0.80 & 0.20 & 0.0005 & 4.3 \times 10^{-6} \\ \hline\end{array}$$ (a) What is the order of the reaction with respect to each reactant? (b) Write the rate expression for the reaction. (c) Calculate \(k\). (d) What is the rate of the reaction when \(\left[\mathrm{H}^{+}\right]=0.933 M\) and \(\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]=3\left[\mathrm{H}^{+}\right]=10\left[\mathrm{I}^{-}\right] ?\)

For the first-order thermal decomposition of ozone $$\mathrm{O}_{3}(g) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)$$ \(k=3 \times 10^{-26} \mathrm{~s}^{-1}\) at \(25^{\circ} \mathrm{C}\). What is the half-life for this reaction in years? Comment on the likelihood that this reaction contributes to the depletion of the ozone layer.

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] \(=0.0500 M\).

See all solutions

Recommended explanations on Chemistry Textbooks

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.