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Chapter 19: Problem 53

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system? (b) For a certain process that occurs at constant \(T\) and \(P\), the value of \(\Delta G\) is positive. Is the process spontaneous? (c) If \(\Delta G\) for a process is large, is the rate at which it occurs fast?

Short Answer

Expert verified
(a) The change in Gibbs free energy (ΔG) does depend on changes in the enthalpy (ΔH) and entropy (ΔS) of the system, as described by the equation: \(ΔG = ΔH - TΔS\), where the process occurs at constant temperature (T). (b) A process with a positive ΔG at constant T and P is considered non-spontaneous, as ΔG should be negative for a process to be spontaneous. (c) A large ΔG value indicates a more significant thermodynamic driving force for the process but doesn't necessarily mean the rate of the process is fast. The rate is determined by reaction kinetics, which are governed by activation energy and the reaction mechanism.

Step by step solution

01

(a) Relationship of ΔG with ΔH and ΔS at constant temperature

The Gibbs free energy change (ΔG) is related to the enthalpy change (ΔH) and entropy change (ΔS) according to the equation: \[ ΔG = ΔH - TΔS \] In this case, the process occurs at constant temperature (T). Thus, the change in Gibbs free energy (ΔG) does depend on changes in the enthalpy (ΔH) and entropy (ΔS) of the system.
02

(b) Spontaneity of process with positive ΔG

A process with positive ΔG is considered to be non-spontaneous at constant T and P. This is because, according to the equation: \[ ΔG = ΔH - TΔS \] when ΔG is positive, it indicates unfavorable thermodynamic conditions for the process to be spontaneous. Remember that for a process to be spontaneous, ΔG should be negative.
03

(c) Relationship of ΔG magnitude with the rate of the process

The magnitude of ΔG doesn't determine the rate at which the process occurs, but rather the thermodynamic favorability or feasibility of the reaction. A large ΔG value indicates a more significant thermodynamic driving force for the process in either the forward or reverse direction (based on the sign of ΔG). To determine the rate of the process, we need to consider the reaction kinetics, which are governed by the activation energy and the reaction mechanism. So, having a large (positive or negative) ΔG doesn't necessarily mean the rate of the process is fast.

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Most popular questions from this chapter

Indicate whether each statement is true or false. (a) The third law of thermodynamics says that the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal. (b) "Translational motion" of molecules refers to their change in spatial location as a function of time. (c) "Rotational" and "vibrational" motions contribute to the entropy in atomic gases like He and Xe. (d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.

(a) Using data in Appendix \(C\), estimate the temperature at which the free- energy change for the transformation from \(\mathrm{I}_{2}(s)\) to \(\mathrm{I}_{2}(g)\) is zero. (b) Use a reference source, such as Web Elements (www.webelements.com), to find the experimental melting and boiling points of \(I_{2}\). (c) Which of the values in part (b) is closer to the value you obtained in part (a)?

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?

For each of the following pairs, predict which substance possesses the larger entropy per mole: (a) \(1 \mathrm{~mol}\) of \(\mathrm{O}_{2}(g)\) at \(300^{\circ} \mathrm{C}, 1.013 \mathrm{kPa},\) or \(1 \mathrm{~mol}\) of \(\mathrm{O}_{3}(g)\) at \(300^{\circ} \mathrm{C}, 1.013 \mathrm{kPa} ;\) (b) \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}(g)\) at $100^{\circ} \mathrm{C}, 101.3 \mathrm{kPa}\(, or \)1 \mathrm{~mol}\( of \)\mathrm{H}_{2} \mathrm{O}(l)$ at $100^{\circ} \mathrm{C}, 101.3 \mathrm{kPa} ;(\mathbf{c}) 0.5 \mathrm{~mol}\( of \)\mathrm{N}_{2}(g)\( at \)298 \mathrm{~K}, 20-\mathrm{L}$. vol- ume, or \(0.5 \mathrm{~mol} \mathrm{CH}_{4}(g)\) at $298 \mathrm{~K}, 20-\mathrm{L}$ volume; (d) \(100 \mathrm{~g}\) \(\mathrm{Na}_{2} \mathrm{SO}_{4}(s)\) at \(30^{\circ} \mathrm{C}\) or $100 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\( at \)30^{\circ} \mathrm{C}$

Carbon disulfide \(\left(C S_{2}\right)\) is a toxic, highly flammable substance. The following thermodynamic data are available for \(\mathrm{CS}_{2}(I)\) and \(\mathrm{CS}_{2}(g)\) at \(298 \mathrm{~K}\) \begin{tabular}{lcc} \hline & \(\Delta H_{i}(\mathrm{k} / \mathrm{mol})\) & $\Delta G_{i}^{\prime}(\mathrm{kJ} / \mathrm{mol})$ \\ \hline\(C S_{2}(l)\) & 89.7 & 65.3 \\ \(C S_{2}(g)\) & 117.4 & 67.2 \\ \hline \end{tabular} (a) Draw the Lewis structure of the molecule. What do you predict for the bond order of the \(\mathrm{C}-\mathrm{S}\) bonds? \((\mathbf{b})\) Use the VSEPR method to predict the structure of the \(\mathrm{CS}_{2}\) molecule. (c) Liquid \(\mathrm{CS}_{2}\) burns in \(\mathrm{O}_{2}\) with a blue flame, forming \(\mathrm{CO}_{2}(g)\) and \(\mathrm{SO}_{2}(g)\). Write a balanced equation for this reaction. (d) Using the data in the preceding table and in Appendix \(C,\) calculate \(\Delta H^{\circ}\) and \(\Delta G^{\circ}\) for the reaction in part \((c) .\) Is the reaction exothermic? Is it spontaneous at \(298 \mathrm{~K} ?\) (e) Use the data in the table to calculate \(\Delta S^{\circ}\) at $298 \mathrm{~K}\( for the vaporization of \)\mathrm{CS}_{2}(I) .$ Is the sign of \(\Delta S^{\circ}\) as you would expect for a vaporization? (f) Using data in the table and your answer to part (e), estimate the boiling point of \(\mathrm{CS}_{2}(l)\). Do you predict that the substance will be a liquid or a gas at \(298 \mathrm{~K}\) and \(101.3 \mathrm{kPa}\) ?
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