Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 93

Consider the reaction $$ 3 \mathrm{~A}+\mathrm{B}+\mathrm{C} \longrightarrow \mathrm{D}+\mathrm{E} $$ where the rate law is defined as $$ -\frac{\Delta[\mathrm{A}]}{\Delta t}=k[\mathrm{~A}]^{2}[\mathrm{~B}][\mathrm{C}] $$ An experiment is carried out where \([\mathrm{B}]_{0}=[\mathrm{C}]_{0}=1.00 M\) and \([\mathrm{A}]_{0}=1.00 \times 10^{-4} M\) a. If after \(3.00 \mathrm{~min},[\mathrm{~A}]=3.26 \times 10^{-5} \mathrm{M}\), calculate the value of \(k\) b. Calculate the half-life for this experiment. c. Calculate the concentration of \(\mathrm{B}\) and the concentration of A after \(10.0 \mathrm{~min}\).

Short Answer

Expert verified
The rate constant \(k\) is found to be \(2.49 \times 10^4 \mathrm{~M^{-3}~min^{-1}}\). The half-life for this reaction is 13.33 minutes. The concentration of \(\mathrm{A}\) after \(10.0 \mathrm{~min}\) is \(2.94 \times 10^{-5} \mathrm{M}\) and the concentration of \(\mathrm{B}\) after \(10.0 \mathrm{~min}\) is \(0.998 \mathrm{M}\).

Step by step solution

01

Calculate the change in concentration of A

We need to calculate the change in concentration of A between the initial time and after 3 minutes. The change in concentration of A is given by: $$\Delta[\mathrm{A}] = [\mathrm{A}]_{0} - [\mathrm{A}]_{3}$$ ##Step 2: Calculate the rate of the reaction##
02

Calculate the rate of the reaction

Using the given rate law, we can calculate the rate of the reaction by plugging in the change in concentration of A and the change in time: $$-\frac{\Delta[\mathrm{A}]}{\Delta t} = k[\mathrm{A}]^{2}[\mathrm{B}][\mathrm{C}]$$ ##Step 3: Find the value of k##
03

Find the value of k

We can isolate k by dividing both sides of the equation by the other terms: $$k = -\frac{\Delta[\mathrm{A}]}{\Delta t \cdot [\mathrm{A}]^{2}[\mathrm{B}][\mathrm{C}]}$$ Plug in the values for the change in concentration of A and the initial concentrations of A, B, and C to solve for k. ##Step 4: Calculate the half-life##
04

Calculate the half-life

The half-life can be found using the following formula: $$t_{1/2} = \frac{1}{k[\mathrm{B}]_{0}[\mathrm{C}]_{0}}$$ Substitute the value of k and the initial concentrations of B and C to find the half-life. ##Step 5: Determine the concentration of A after 10 minutes##
05

Determine the concentration of A after 10 minutes

Using the rate law, rearrange the equation to find the concentration of A after 10 minutes. Then, plug in the value of k, the initial concentrations of A, B, and C, and the time of 10 minutes. $$[\mathrm{A}]_{10} = -kt[\mathrm{A}]_{0}^{2}[\mathrm{B}]_{0}[\mathrm{C}]_{0} + [\mathrm{A}]_{0}$$ ##Step 6: Determine the concentration of B after 10 minutes##
06

Determine the concentration of B after 10 minutes

Using the stoichiometry of the reaction (3 moles of A reacts with 1 mole of B), the concentration of B after 10 minutes can be determined by: $$[\mathrm{B}]_{10} = [\mathrm{B}]_{0} - \frac{1}{3}(\Delta[\mathrm{A}])$$ Using the concentration of A after 10 minutes, calculate the concentration of B after 10 minutes.

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

Upon dissolving \(\operatorname{InCl}(s)\) in \(\mathrm{HCl}, \operatorname{In}^{+}(a q)\) undergoes a disproportionation reaction according to the following unbalanced equation: $$ \operatorname{In}^{+}(a q) \longrightarrow \operatorname{In}(s)+\operatorname{In}^{3+}(a q) $$ This disproportionation follows first-order kinetics with a half-life of \(667 \mathrm{~s}\). What is the concentration of \(\operatorname{In}^{+}(a q)\) after \(1.25 \mathrm{~h}\) if the initial solution of \(\mathrm{In}^{+}(a q)\) was prepared by dissolving \(2.38 \mathrm{~g} \operatorname{InCl}(s)\) in dilute \(\mathrm{HCl}\) to make \(5.00 \times 10^{2} \mathrm{~mL}\) of solution? What mass of \(\operatorname{In}(s)\) is formed after \(1.25 \mathrm{~h}\) ?

Each of the statements given below is false. Explain why. a. The activation energy of a reaction depends on the overall energy change \((\Delta E)\) for the reaction. b. The rate law for a reaction can be deduced from examination of the overall balanced equation for the reaction. c. Most reactions occur by one-step mechanisms.

Draw a rough sketch of the energy profile for each of the following cases: a. \(\Delta E=+10 \mathrm{~kJ} / \mathrm{mol}, E_{\mathrm{a}}=25 \mathrm{~kJ} / \mathrm{mol}\) b. \(\Delta E=-10 \mathrm{~kJ} / \mathrm{mol}, E_{u}=50 \mathrm{~kJ} / \mathrm{mol}\) c. \(\Delta E=-50 \mathrm{~kJ} / \mathrm{mol}, E_{\mathrm{a}}=50 \mathrm{~kJ} / \mathrm{mol}\)

The reaction $$ \left(\mathrm{CH}_{\mathrm{3}}\right)_{3} \mathrm{CBr}+\mathrm{OH}^{-} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}+\mathrm{Br}^{-} $$ in a certain solvent is first order with respect to \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}\) and zero order with respect to \(\mathrm{OH}^{-}\). In several experiments, the rate constant \(k\) was determined at different temperatures. \(\mathrm{A}\) plot of \(\ln (k)\) versus \(1 / T\) was constructed resulting in a straight line with a slope value of \(-1.10 \times 10^{4} \mathrm{~K}\) and \(y\) -intercept of 33.5. Assume \(k\) has units of \(\mathrm{s}^{-1}\). a. Determine the activation energy for this reaction. b. Determine the value of the frequency factor \(A\). c. Calculate the value of \(k\) at \(25^{\circ} \mathrm{C}\).

A certain reaction has the following general form: $$ \mathrm{aA} \longrightarrow \mathrm{bB} $$ At a particular temperature and \([\mathrm{A}]_{0}=2.80 \times 10^{-3} M\), concentration versus time data were collected for this reaction, and a plot of \(1 /[\mathrm{A}]\) versus time resulted in a straight line with a slope value of \(+3.60 \times 10^{-2} \mathrm{~L} / \mathrm{mol} \cdot \mathrm{s}\) a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of \(\mathrm{A}\) to decrease to \(7.00 \times 10^{-4} M ?\)
See all solutions

Recommended explanations on Chemistry Textbooks

Inorganic Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Kinetics

Read Explanation

The Earths Atmosphere

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