Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Problem 99

At \(800 \mathrm{~K},\) the equilibrium constant for the reaction \(\mathrm{A}_{2}(g) \rightleftharpoons 2 \mathrm{~A}(g)\) is $K_{c}=3.1 \times 10^{-4}$. (a) Assuming both forward and reverse reactions are elementary reactions, which rate constant do you expect to be larger, \(k_{f}\) or \(k_{r} ?\) (b) If the value of $k_{f}=0.27 \mathrm{~s}^{-1}\(, what is the value of \)k_{r}\( at \)800 \mathrm{~K} ?$ (c) Based on the nature of the reaction, do you expect the forward reaction to be endothermic or exothermic? (d) If the temperature is raised to $1000 \mathrm{~K}\(, will the reverse rate constant \)k_{r}$ increase or decrease? Will the change in \(k_{r}\) be larger or smaller than the change in \(k_{f}\) ?

Short Answer

Expert verified
(a) At 800 K, the rate constant \(k_r\) is larger than \(k_f\), as the equilibrium constant Kc is less than 1. (b) The value of \(k_r\) at 800 K is approximately 870.97 s⁻¹. (c) The forward reaction is endothermic, as the reaction favors the reactant side (A2) more than the product side (A). (d) If the temperature is raised to 1000 K, the reverse rate constant \(k_r\) will decrease, and the change in \(k_r\) will be smaller than the change in \(k_f\).

Step by step solution

01

Understand the relationship between equilibrium constant and rate constants

The equilibrium constant (Kc) is related to the forward reaction rate constant (kf) and reverse reaction rate constant (kr) by the following equation: \[ K_c = \frac{k_f}{k_r} \] (a)
02

Determine which rate constant will be larger

We know that the equilibrium constant Kc is equal to 3.1 x 10⁻⁴ for the reaction at 800 K. Since Kc is less than 1, this means that kf must be smaller than kr. Therefore, we expect kr to be larger than kf. (b)
03

Calculate the value of kr

Given that kf = 0.27 s⁻¹, we can use the relationship between Kc, kf, and kr to solve for kr: \[ k_r = \frac{k_f}{K_c} \] Substitute the given values, \[ k_r = \frac{0.27 \mathrm{~s}^{-1}}{3.1 \times 10^{-4}}\] Now, calculate kr, \[ k_r \approx 870.97 \mathrm{~s}^{-1} \] (c)
04

Determine the nature of the reaction (endothermic or exothermic)

Since the equilibrium constant Kc is less than 1 and kr is larger than kf, this indicates that the reaction favors the reactant side (A2) more than the product side (A). This suggests that the forward reaction requires energy input, making it endothermic. (d)
05

Effect of increasing temperature on the reverse rate constant kr

Increasing the temperature tends to favor endothermic reactions, shifting the equilibrium towards the products. As a result, the reverse rate constant kr would decrease. The change in kf would be larger than the change in kr, as the forward reaction is endothermic and will be more sensitive to the increase in temperature.

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

For the reaction $\mathrm{I}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \operatorname{IBr}(g), K_{c}=310\( at \)140^{\circ} \mathrm{C}$. Suppose that \(1.00 \mathrm{~mol}\) IBr in a \(5.00-\mathrm{L}\) flask is allowed to reach equilibrium at \(140^{\circ} \mathrm{C}\). What are the equilibrium concentrations of \(\mathrm{IBr}, \mathrm{I}_{2},\) and \(\mathrm{Br}_{2}\) ?

As shown in Table \(15.2,\) the equilibrium constant for the reaction $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\( is \)K_{p}=4.23 \times 10^{-7}\( at \)300^{\circ} \mathrm{C}\(. Pure \)\mathrm{NH}_{3}$ is placed in a 1.00-L flask and allowed to reach equilibrium at this temperature. There are $1.05 \mathrm{~g} \mathrm{NH}_{3}$ in the equilibrium mixture. (a) What are the masses of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) in the equilibrium mixture? (b) What was the initial mass of ammonia placed in the vessel? (c) What is the total pressure in the vessel?

A chemist at a pharmaceutical company is measuring equilibrium constants for reactions in which drug candidate molecules bind to a protein involved in cancer. The drug molecules bind the protein in a 1: 1 ratio to form a drug- protein complex. The protein concentration in aqueous solution at $25^{\circ} \mathrm{C}\( is \)1.50 \times 10^{-6} \mathrm{M}$. Drug A is introduced into the protein solution at an initial concentration of $2.00 \times 10^{-6} \mathrm{M}$. Drug B is introduced into a separate, identical protein solution at an initial concentration of \(2.00 \times 10^{-6} \mathrm{M}\). At equilibrium, the drug A-protein solution has an A-protein complex concentration of \(1.00 \times 10^{-6} \mathrm{M}\), and the drug \(\mathrm{B}\) solution has a B-protein complex concentration of $1.40 \times 10^{-6} \mathrm{M}\(. Calculate the \)K_{c}$ value for the A-protein binding reaction and for the B-protein binding reaction. Assuming that the drug that binds more strongly will be more effective, which drug is the better choice for further research?

Write the expressions for \(K_{c}\) for the following reactions. In each case indicate whether the reaction is homogeneous or heterogeneous. (a) \(\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}(g)\) (b) $\mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)$ (c) $\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)$ (d) $\mathrm{O}_{2}(g)+2 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g)$ (e) $\mathrm{HCO}_{3}^{-}(a q) \rightleftharpoons \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}^{+}(a q)$ (f) $\mathrm{Fe}^{2+}(a q)+\mathrm{Ce}^{4+}(a q) \rightleftharpoons \mathrm{Fe}^{3+}(a q)+\mathrm{Ce}^{3+}(a q)$ (g) $\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$

(a) Is the dissociation of fluorine molecules into atomic fluorine, \(\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{~F}(g)\) an exothermic or endothermic process? (b) If the temperature is raised by \(100 \mathrm{~K}\), does the equilibrium constant for this reaction increase or decrease? (c) If the temperature is raised by \(100 \mathrm{~K},\) does the forward rate constant \(k_{f}\) increase by a larger or smaller amount than the reverse rate constant \(k_{r} ?\)
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Ionic and Molecular Compounds

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