Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Problem 25

(a) Consider the combustion of \(\mathrm{H}_{2}(g): 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) \(\longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) .\) If hydrogen is burning at the rate of 0.48 \(\mathrm{mol} / \mathrm{s}\), what is the rate of consumption of oxygen? What is the rate of formation of water vapor? (b) The reaction \(2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)\) is carried out in a closed vessel. If the partial pressure of \(\mathrm{NO}\) is decreasing at the rate of 56 torr \(/ \mathrm{min}\), what is the rate of change of the total pressure of the vessel?

Short Answer

Expert verified
The rate of consumption of oxygen is \(0.24 \, mol/s\) and the rate of formation of water vapor is \(0.48 \, mol/s\). The rate of change of total pressure of the vessel is \(-28 \, torr/min\).

Step by step solution

01

Identify the stoichiometric coefficients

In the balanced combustion of hydrogen, we have the equation as: \(2 H_{2}(g) + O_{2}(g) \longrightarrow 2 H_{2}O(g)\) Here, the stoichiometric coefficients are 2 for hydrogen, 1 for oxygen, and 2 for water vapor.
02

Relate the rates using stoichiometry

We can relate the rate of consumption of hydrogen, oxygen, and formation of water vapor using their stoichiometric coefficients: \(\frac{d[H_2]}{dt} : \frac{d[O_2]}{dt} : \frac{d[H_2O]}{dt} = -2 : -1 : 2\)
03

Calculate the rate of consumption of oxygen

The given rate of consumption of hydrogen is 0.48 mol/s: \(\frac{d[H_2]}{dt} = -0.48 \, mol/s\) Using the ratio from Step 2, we can calculate the rate of consumption of oxygen: \(\frac{d[O_2]}{dt} = (-0.48 * (-1))/(-2) = 0.24 \, mol/s\)
04

Calculate the rate of formation of water vapor

Similarly, using the ratio from Step 2, we can calculate the rate of formation of water vapor: \(\frac{d[H_2O]}{dt} = (-0.48 * 2)/(-2) = 0.48 \, mol/s\) b) Rate of change of the total pressure of the vessel
05

Identify the stoichiometric coefficients

In the balanced reaction, we have the equation as: \(2 NO(g) + Cl_2(g) \longrightarrow 2 NOCl(g)\) Here, the stoichiometric coefficients are 2 for NO, 1 for Cl₂, and 2 for NOCl.
06

Relate the rates using stoichiometry

We can relate the rate of consumption of NO, Cl₂, and formation of NOCl using their stoichiometric coefficients: \(\frac{d[NO]}{dt} : \frac{d[Cl_2]}{dt} : \frac{d[NOCl]}{dt} = -2 : -1 : 2\)
07

Calculate the rate of consumption of Cl₂ and formation of NOCl

The given rate of decrease in partial pressure of NO is 56 torr/min: \(\frac{d[P_{NO}]}{dt} = -56 \, torr/min\) Using the ratio from Step 2, we can calculate the rate of consumption of Cl₂ and formation of NOCl: \(\frac{d[P_{Cl_2}]}{dt} = (-56 * (-1))/(-2) = -28 \, torr/min\) \(\frac{d[P_{NOCl}]}{dt} = (-56 * 2)/(-2) = 56 \, torr/min\)
08

Calculate the rate of change of the total pressure

Now, we can calculate the rate of change of the total pressure of the vessel by adding the rates of change in partial pressures: \(\frac{d[P_{total}]}{dt} = \frac{d[P_{NO}]}{dt} + \frac{d[P_{Cl_2}]}{dt} + \frac{d[P_{NOCl}]}{dt} = -56 \, torr/min - 28 \, torr/min + 56 \, torr/min = -28 \, torr/min\) So, the rate of change of the total pressure of the vessel is -28 torr/min.

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

The temperature dependence of the rate constant for a reaction is tabulated as follows: $$ \begin{array}{lc} \hline \text { Temperature (K) } & k\left(M^{-1} \mathrm{~s}^{-1}\right) \\ \hline 600 & 0.028 \\ 650 & 0.22 \\ 700 & 1.3 \\ 750 & 6.0 \\ 800 & 23 \\ \hline \end{array} $$ Calculate \(E_{a}\) and \(A\).

Americium-241 is used in smoke detectors. It has a first order rate constant for radioactive decay of \(k=1.6 \times 10^{-3} \mathrm{yr}^{-1}\). By contrast, iodine- \(125,\) which is used to test for thyroid functioning, has a rate constant for radioactive decay of \(k=0.011\) day \(^{-1}\). (a) What are the halflives of these two isotopes? (b) Which one decays at a faster rate? (c) How much of a 1.00 -mg sample of each isotope remains after 3 half-lives? (d) How much of a 1.00 -mg sample of each isotope remains after 4 days?

The rate of the reaction $$ \begin{aligned} \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(a q)+\mathrm{OH}^{-}(a q) & \longrightarrow \\ \mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \end{aligned} $$ was measured at several temperatures, and the following data were collected: $$ \begin{array}{ll} \hline \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & \boldsymbol{k}\left(\boldsymbol{M}^{-1} \mathrm{~s}^{-1}\right) \\ \hline 15 & 0.0521 \\ 25 & 0.101 \\ 35 & 0.184 \\ 45 & 0.332 \\ \hline \end{array} $$ Calculate the value of \(E_{a}\) by constructing an appropriate graph.

You have studied the gas-phase oxidation of \(\mathrm{HBr}\) by \(\mathrm{O}_{2}\) : $$ 4 \mathrm{HBr}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{Br}_{2}(g) $$ You find the reaction to be first order with respect to HBr and first order with respect to \(\mathrm{O}_{2}\). You propose the following mechanism: $$ \begin{aligned} \mathrm{HBr}(g)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{HOOBr}(g) \\ \mathrm{HOOBr}(g)+\mathrm{HBr}(g) & \longrightarrow 2 \mathrm{HOBr}(g) \\ \mathrm{HOBr}(g)+\mathrm{HBr}(g) & \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Br}_{2}(g) \end{aligned} $$ (a) Confirm that the elementary reactions add to give the overall reaction. (b) Based on the experimentally determined rate law, which step is rate determining? (c) What are the intermediates in this mechanism? (d) If you are unable to detect HOBr or HOOBr among the products, does this disprove your mechanism?

Many metallic catalysts, particularly the precious-metal ones, are often deposited as very thin films on a substance of high surface area per unit mass, such as alumina \(\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)\) or silica \(\left(\mathrm{SiO}_{2}\right)\). (a) Why is this an effective way of utilizing the catalyst material compared to having powdered metals? (b) How does the surface area affect the rate of reaction?
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Chemistry Branches

Read Explanation

Chemical Reactions

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Making Measurements

Read Explanation

Chemical Analysis

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