Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 19: Problem 36

Calculate the equilibrium constant and Gibbs energy for the reaction \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})\) at \(483 \mathrm{K}\) by using the data tables from Appendix D. Are the values determined here different from or the same as those in exercise \(35 ?\) Explain.

Short Answer

Expert verified
The Gibbs energy and equilibrium constant for the reaction are calculated from the provided data in Appendix D. We then compare the obtained values to those from exercise 35 to determine if they are the same or different.

Step by step solution

01

Identify the relevant data from Appendix D

Identify the standard Gibbs free energy of formation(\( \Delta G_{f}^{0} \)) for each compound involved in the reaction from the Appendix D. These values should be provided for the compounds CO, H2, and CH3OH at the temperature of 483K.
02

Calculate the Gibbs free energy(ΔG) for the reaction

Calculate the standard Gibbs free energy of the reaction (\( \Delta G^{0} \)) using the equation \( \Delta G^{0} = \sum \Delta G_{f}^{0} (products) - \sum \Delta G_{f}^{0} (reactants) \). Here, multiply the \( \Delta G_{f}^{0} \) value of each compound by its stoichiometric coefficient in the balanced chemical equation.
03

Calculate the equilibrium constant (K)

Use the obtained value of \( \Delta G^{0} \) to calculate the equilibrium constant (K) for the reaction at the given temperature. The Van't Hoff Equation relates these two quantities: \( \Delta G^{0} = -RT \ln K \), where R is the gas constant (8.314 J/mol*K) and T is the absolute temperature in Kelvin. Solving for K gives \( K = e^{-\Delta G^{0}/RT} \) .
04

Compare the results with exercise 35

Compare the calculated values of \( \Delta G^{0} \) and K for this reaction with the values obtained in exercise 35. Express whether they match or differ and offer a probable explanation why.

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 following standard Gibbs energy changes are given for \(25^{\circ} \mathrm{C}\) (1) \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})\) \(\Delta G^{\circ}=-33.0 \mathrm{kJ}\) (2) \(4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(1)\) \(\Delta G^{\circ}=-1010.5 \mathrm{kJ}\) (3) \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})\) \(\Delta G^{\circ}=+173.1 \mathrm{kJ}\) (4) \(\mathrm{N}_{2}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\) \(\Delta G^{\circ}=+102.6 \mathrm{kJ}\) (5) \(2 \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{N}_{2} \mathrm{O}(\mathrm{g})\) \(\Delta G^{\circ}=+208.4 \mathrm{kJ}\) Combine the preceding equations, as necessary, to obtain \(\Delta G^{\circ}\) values for each of the following reactions. (a) \(\mathrm{N}_{2} \mathrm{O}(\mathrm{g})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \quad \Delta G^{\circ}=?\) (b) \(2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(1) \quad \Delta G^{\circ}=?\) (c) \(2 \mathrm{NH}_{3}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(1)\) \(\Delta G^{\circ}=?\) Of reactions (a), (b), and (c), which would tend to go to completion at \(25^{\circ} \mathrm{C}\), and which would reach an equilibrium condition with significant amounts of all reactants and products present?

Use the following data to estimate the standard molar entropy of gaseous benzene at \(298.15 \mathrm{K} ;\) that is, \(S^{\circ}\left[\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{g}, 1 \mathrm{atm})\right] .\) For \(\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{s}, 1 \mathrm{atm})\) at its melting point of \(5.53^{\circ} \mathrm{C}, S^{\circ}\) is \(128.82 \mathrm{Jmol}^{-1} \mathrm{K}^{-1}\). The enthalpy of fusion is \(9.866 \mathrm{kJ} \mathrm{mol}^{-1} .\) From the melting point to 298.15 K, the average heat capacity of liquid benzene is \(134.0 \mathrm{JK}^{-1} \mathrm{mol}^{-1} .\) The enthalpy of vaporization of \(\mathrm{C}_{6} \mathrm{H}_{6}(1)\) at \(298.15 \mathrm{K}\) is \(33.85 \mathrm{kJ} \mathrm{mol}^{-1},\) and in the vapor- ization, \(\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{g})\) is produced at a pressure of 95.13 Torr. Imagine that this vapor could be compressed to 1 atm pressure without condensing and while behaving as an ideal gas. Calculate \(S^{\circ}\left[\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{g}, 1 \text { atm) }] .[ \text { Hint: Refer to }\right.\) Exercise \(88,\) and note the following: For infinitesimal quantities, \(d S=d q / d T ;\) for the compression of an ideal gas, \(d q=-d w ;\) and for pressure-volume work, \(d w=-P d V\).

\(\mathrm{H}_{2}(\mathrm{g})\) can be prepared by passing steam over hot iron: \(3 \mathrm{Fe}(\mathrm{s})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})+4 \mathrm{H}_{2}(\mathrm{g})\) (a) Write an expression for the thermodynamic equilibrium constant for this reaction. (b) Explain why the partial pressure of \(\mathrm{H}_{2}(\mathrm{g})\) is independent of the amounts of \(\mathrm{Fe}(\mathrm{s})\) and \(\mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})\) present. (c) Can we conclude that the production of \(\mathrm{H}_{2}(\mathrm{g})\) from \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) could be accomplished regardless of the proportions of \(\mathrm{Fe}(\mathrm{s})\) and \(\mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})\) present? Explain.

From the data given in the following table, determine \(\Delta S^{\circ} \quad\) for the reaction \(\quad \mathrm{NH}_{3}(\mathrm{g})+\mathrm{HCl}(\mathrm{g}) \longrightarrow\) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s}) .\) All data are at \(298 \mathrm{K}\) $$\begin{array}{lcc} \hline & \Delta H_{f}^{\circ}, \mathrm{kJ} \mathrm{mol}^{-1} & \Delta G_{f,}^{\circ} \mathrm{kJ} \mathrm{mol}^{-1} \\ \hline \mathrm{NH}_{3}(\mathrm{g}) & -46.11 & -16.48 \\ \mathrm{HCl}(\mathrm{g}) & -92.31 & -95.30 \\ \mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s}) & -314.4 & -202.9 \\ \hline \end{array}$$

In biochemical reactions the phosphorylation of amino acids is an important step. Consider the following two reactions and determine whether the phosphorylation of arginine with ATP is spontaneous. $$\begin{array}{c} \mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{ADP}+\mathrm{P} \quad \Delta G^{\circ \prime}=-31.5 \mathrm{kJ} \mathrm{mol}^{-1} \\ \text {arginine }+\mathrm{P} \longrightarrow \text { phosphorarginine }+\mathrm{H}_{2} \mathrm{O} \\ \Delta G^{\circ \prime}=33.2 \mathrm{kJ} \mathrm{mol}^{-1} \end{array}$$
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Making Measurements

Read Explanation

Chemical Analysis

Read Explanation

Chemical Reactions

Read Explanation

Physical Chemistry

Read Explanation

Organic 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