Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 56

The decomposition of nitrosyl chloride $$\mathrm{NOCl}(g) \longrightarrow \mathrm{NO}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g)$$ is a second-order reaction. If it takes \(0.20 \mathrm{~min}\) to decompose \(15 \%\) of a \(0.300 \mathrm{M}\) solution of nitrosyl chloride, what is \(k\) for the reaction?

Short Answer

Expert verified
Answer: The reaction rate constant (k) for the decomposition of nitrosyl chloride is approximately 0.0536 M⁻¹s⁻¹.

Step by step solution

01

Write down the integrated rate law for a second-order reaction

The integrated rate law for a second-order reaction is given by: $$\frac{1}{[\mathrm{A}]_{t}}=\frac{1}{[\mathrm{A}]_{0}}+kt$$ where \([\mathrm{A}]_{t}\) is the concentration of \(\mathrm{A}\) at time \(t\), \([\mathrm{A}]_{0}\) is the initial concentration of \(\mathrm{A}\), \(k\) is the reaction rate constant, and \(t\) is the time elapsed.
02

Determine the initial concentration and the concentration at the given time

We are told the initial concentration of nitrosyl chloride is \([\mathrm{NOCl}]_{0}=0.300\,\mathrm{M}\). Since we need to find the concentration after decomposing \(15\%\) of the initial concentration, we have: $$[\mathrm{NOCl}]_{t}=0.85\times[\mathrm{NOCl}]_{0}=0.85\times0.300\,\mathrm{M}=0.255\,\mathrm{M}$$
03

Determine the given time and convert it to the appropriate unit

The given time for the decomposition is \(0.20\,\mathrm{minutes}\), which needs to be converted to seconds: $$t=0.20\,\mathrm{minutes}\times\frac{60\,\mathrm{s}}{1\,\mathrm{min}}=12\,\mathrm{s}$$
04

Plug the values into the integrated rate law and solve for k

Now, we can plug in the values for \([\mathrm{NOCl}]_{0}\), \([\mathrm{NOCl}]_{t}\), and \(t\) into the integrated rate law and solve for \(k\): $$\frac{1}{0.255\,\mathrm{M}}=\frac{1}{0.300\,\mathrm{M}}+k(12\,\mathrm{s})$$ Solving for \(k\) yields: $$k=\frac{\frac{1}{0.255\,\mathrm{M}}-\frac{1}{0.300\,\mathrm{M}}}{12\,\mathrm{s}}\approx0.0536\,\mathrm{M^{-1}s^{-1}}$$ So, the reaction rate constant for the decomposition of nitrosyl chloride is approximately \(k=0.0536\,\mathrm{M^{-1}s^{-1}}\).

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

Two mechanisms are proposed for the reaction $$\begin{array}{cl}2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) & \\ \text { Mechanism 1: } \mathrm{NO}+\mathrm{O}_{2} \rightleftharpoons \mathrm{NO}_{3} & \text { (fast) } \\ \mathrm{NO}_{3}+\mathrm{NO} \longrightarrow 2 \mathrm{NO}_{2} & \text { (slow) } \\ \text { Mechanism 2: } \mathrm{NO}+\mathrm{NO} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2} & \text { (fast) } \\ \mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{NO}_{2} & \text { (slow) } \end{array}$$ Show that each of these mechanisms is consistent with the observed rate law: rate \(=k[\mathrm{NO}]^{2} \times\left[\mathrm{O}_{2}\right]\).

For the reaction $$2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ the experimental rate expression is rate \(=k[\mathrm{NO}]^{2} \times\left[\mathrm{H}_{2}\right] .\) The following mechanism is proposed: $$\begin{array}{cc}2 \mathrm{NO} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{2} & \text { (fast) } \\ \mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{N}_{2} \mathrm{O} & \text { (slow) } \\ \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O} & \text { (fast) } \end{array}$$ Is this mechanism consistent with the rate expression?

For a reaction involving the decomposition of \(\mathrm{Y}\), the following data are obtained: $$\begin{array}{lllll}\hline \text { Rate }(\mathrm{mol} / \mathrm{L} \cdot \min ) & 0.288 & 0.245 & 0.202 & 0.158 \\ {[\mathrm{Y}]} & 0.200 & 0.170 & 0.140 & 0.110 \\ \hline\end{array}$$ (a) Determine the order of the reaction. (b) Write the rate expression for the decomposition of Y. (c) Calculate \(k\) for the experiment above.

For the zero-order decomposition of ammonia on tungsten $$\mathrm{NH}_{3}(\mathrm{~g}) \stackrel{\mathrm{w}}{\longrightarrow} \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g)$$ the rate constant is \(2.08 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\). (a) What is the half-life of a \(0.250 \mathrm{M}\) solution of ammonia? (b) How long will it take for the concentration of ammonia to drop from \(1.25 M\) to \(0.388 M ?\)

Argon- 41 is used to measure the rate of gas flow. It has a decay constant of \(6.3 \times 10^{-3} \mathrm{~min}^{-1}\). (a) What is its half-life? (b) How long will it take before only \(1.00 \%\) of the original amount of Ar- 41 is left?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Chemical Reactions

Read Explanation

Making Measurements

Read Explanation

Physical 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