Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 19: Problem 55

For a certain chemical reaction, $\Delta H^{\circ}=-40.0 \mathrm{k} \mathrm{J}\( and \)\Delta S^{\circ}=-150.0 \mathrm{~J} / \mathrm{K}$. (a) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the surroundings? (c) Calculate \(\Delta G^{\circ}\) for the reaction at \(298 \mathrm{~K}\). (d) Is the reaction spontaneous at $298 \mathrm{~K}$ under standard conditions?

Short Answer

Expert verified
(a) The reaction leads to a decrease in the randomness or disorder of the system since \(\Delta S^{\circ} = -150.0 \, J/K\), which is negative. (b) The reaction leads to an increase in the randomness or disorder of the surroundings because \(\Delta H^{\circ} = -40.0 \, kJ\), which is negative, meaning heat is released by the system to the surroundings. (c) Using the formula \(\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\), we find \(\Delta G^{\circ} = 4,700 \, J\). (d) The reaction is not spontaneous at \(298 \, K\) under standard conditions since \(\Delta G^{\circ} > 0\).

Step by step solution

01

(a) Effect on the randomness of the system

We are given \(\Delta S^{\circ} = -150.0 \, J/K\). Since \(\Delta S^{\circ}\) represents the change in entropy, a negative value means that the entropy decreases, and there is a decrease in the randomness or disorder of the system.
02

(b) Effect on the randomness of the surroundings

We are given \(\Delta H^{\circ} = -40.0 \, kJ\). \(\Delta H^{\circ}\) represents the change in enthalpy, which is equal to the heat absorbed or released by the system at constant pressure. A negative value means that heat is released by the system to the surroundings. When heat is transferred, the randomness of the surroundings increases.
03

(c) Calculate \(\Delta G^{\circ}\) for the reaction

To calculate \(\Delta G^{\circ}\), we must use the following formula: \[\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\] where \(T\) is the temperature in Kelvin. We are given \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\), and we know the temperature is \(298 K\). So, we can plug in the values and calculate \(\Delta G^{\circ}\): \[\Delta G^{\circ} = (-40.0 \times 10^3 \, J) - (298 \, K)(-150.0 \, J/K) \]
04

Calculate the value for \(\Delta G^{\circ}\)

Now we can compute the result for \(\Delta G^{\circ}\): \[\Delta G^{\circ} = (-40.0 \times 10^3 \, J) + (298 \times 150.0 J) \] \[\Delta G^{\circ} = -40.0 \times 10^3 \, J + 44,700 \, J \] \[\Delta G^{\circ} = -40,000 \, J + 44,700 \, J = 4,700 \, J\]
05

(d) Spontaneity of the reaction

A reaction is spontaneous at a given temperature under standard conditions if \(\Delta G^{\circ} < 0\). In this case, we calculated \(\Delta G^{\circ} = 4,700 \, J\), which is greater than zero. Therefore, the reaction is not spontaneous at \(298 \, K\) under standard conditions.

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

Using the data in Appendix \(C\) and given the pressures listed, calculate \(K_{\mathrm{p}}\) and \(\Delta G\) for each of the following reactions: $$ \begin{array}{l} \text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \\ \quad R_{\mathrm{N}_{2}}=263.4 \mathrm{kPa}, P_{\mathrm{H}_{2}}=597.8 \mathrm{kPa}, P_{\mathrm{NH}_{3}}=101.3 \mathrm{kPa} \\ \text { (b) } 2 \mathrm{~N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{NO}_{2}(g) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \end{array} $$ \(P_{\mathrm{N}_{2} \mathrm{H}_{4}}=P_{\mathrm{NO}_{2}}=5.07 \mathrm{kPa}\) $$ \begin{array}{l} \quad R_{\mathrm{N}_{2}}=50.7 \mathrm{kPa}, P_{\mathrm{H}_{2} \mathrm{O}}=30.4 \mathrm{kPa} \\ \text { (c) } \mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \\ P_{\mathrm{N}_{2} \mathrm{H}_{4}}=101.3 \mathrm{kPa}, P_{\mathrm{N}_{2}}=152.0 \mathrm{kPa}, P_{\mathrm{H}_{2}}=253.3 \mathrm{kPa} \end{array} $$

Using data from Appendix \(\mathrm{C}\), calculate the change in Gibbs free energy for each of the following reactions. In each case, indicate whether the reaction is spontaneous at \(298 \mathrm{~K}\) under standard conditions. (a) \(2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)\) (b) $\mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$ (c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$ (d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)$

Predict which member of each of the following pairs has the greater standard entropy at \(25^{\circ} \mathrm{C}:\) (a) \(\mathrm{HNO}_{3}(g)\) or \(\mathrm{HNO}_{3}(a q)\) (b) \(\mathrm{PCl}_{3}(l)\) or \(\mathrm{PCl}_{3}(g)\), (c) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) or \(\mathrm{Fe}_{3} \mathrm{O}_{4}(s),(\mathbf{d}) \mathrm{Li}(s)\) or \(\mathrm{Li}(g)\). Use Appendix \(\mathrm{C}\) to find the stan- dard entropy of each substance.

Acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\), is used in welding. (a) Write a balanced equation for the combustion of acetylene gas to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .(\mathbf{b})\) How much heat is produced in burning \(1 \mathrm{~mol}\) of $\mathrm{C}_{2} \mathrm{H}_{2}$ under standard conditions if both reactants and products are brought to \(298 \mathrm{~K} ?\) (c) What is the maximum amount of useful work that can be accomplished under standard conditions by this reaction?

A certain reaction has \(\Delta H^{\circ}=+20.0 \mathrm{~kJ}\) and $\Delta S^{\circ}=\( \)+100.0 \mathrm{~J} / \mathrm{K} .$ (a) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the surroundings? (c) Calculate \(\Delta G^{\circ}\) for the reaction at $298 \mathrm{~K} .(\mathbf{d})\( Is the reaction spontaneous at \)298 \mathrm{~K}$ under standard conditions?
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Physical Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

Making Measurements

Read Explanation

Chemical Analysis

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