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Chapter 17: Problem 65

A certain reaction is known to have a \(\Delta G^{\circ}\) value of \(-122 \mathrm{~kJ} / \mathrm{mol} .\) Will the reaction necessarily occur if the reactants are mixed together?

Short Answer

Expert verified
No, the reaction will not necessarily occur even if the \(\Delta G^{\circ}\) value is negative. This is due to the fact that the sign of \(\Delta G\) might change under non-standard conditions.

Step by step solution

01

Understanding Gibbs Free Energy

The Gibbs Free Energy (\(\Delta G\)) is a thermodynamic potential that measures the maximum reversible work that a system can perform at constant temperature and pressure. It is used to determine whether a reaction is spontaneous or not. A reaction is spontaneous if the \(\Delta G\) value is negative, non-spontaneous if it is positive, and in equilibrium if it's zero.
02

Analyzing the Given \(\Delta G^{\circ}\) Value

The given \(\Delta G^{\circ}\) value for the reaction is -122 kJ/mol. A negative \(\Delta G^{\circ}\) indicates that the reaction is spontaneous under standard conditions (298 K and 1 bar pressure).
03

Consider Non-Standard Conditions

However, \(\Delta G^{\circ}\) is the value of \(\Delta G\) under standard conditions. When reactants are mixed together under non-standard conditions, the value of \(\Delta G\) could be different from \(\Delta G^{\circ}\). So, the reaction might not necessarily occur.

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Most popular questions from this chapter

The reaction \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) proceeds spontaneously at \(25^{\circ} \mathrm{C}\) even though there is a decrease in the number of microstates of the system (gases are converted to a solid). Explain.

Entropy has sometimes been described as "time's arrow" because it is the property that determines the forward direction of time. Explain.

Calculate \(\Delta G^{\circ}\) for the following reactions at \(25^{\circ} \mathrm{C}\) : (a) \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow\) $$ 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ See Appendix 2 for thermodynamic data.

A \(74.6-\mathrm{g}\) ice cube floats in the Arctic Sea. The temperature and pressure of the system and surroundings are at 1 atm and \(0^{\circ} \mathrm{C}\). Calculate \(\Delta S_{\text {sys }}, \Delta S_{\text {surr }}\) and \(\Delta S_{\text {univ }}\) for the melting of the ice cube. What can you conclude about the nature of the process from the value of \(\Delta S_{\text {univ }} ?\) (The molar heat of fusion of water is \(6.01 \mathrm{~kJ} / \mathrm{mol} .)\)

Consider two carboxylic acids (acids that contain the \(-\mathrm{COOH}\) group \(): \mathrm{CH}_{3} \mathrm{COOH}\) (acetic acid, \(\left.K_{\mathrm{a}}=1.8 \times 10^{-5}\right)\) and \(\mathrm{CH}_{2} \mathrm{ClCOOH}\) (chloroacetic acid, \(K_{\mathrm{a}}=1.4 \times 10^{-3}\) ). (a) Calculate \(\Delta G^{\circ}\) for the ionization of these acids at \(25^{\circ} \mathrm{C}\). (b) From the equation \(\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ},\) we see that the contributions to the \(\Delta G^{\circ}\) term are an enthalpy term \(\left(\Delta H^{\circ}\right)\) and a temperature times entropy term \(\left(T \Delta S^{\circ}\right) .\) These contributions are listed below for the two acids: $$ \begin{array}{lcc} \hline & \Delta H^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) & T \Delta S^{\circ}(\mathrm{k} \mathrm{J} / \mathrm{mol}) \\ \hline \mathrm{CH}_{3} \mathrm{COOH} & -0.57 & -27.6 \\ \mathrm{CH}_{2} \mathrm{ClCOOH} & -4.7 & -21.1 \\ \hline \end{array} $$ Which is the dominant term in determining the value of \(\Delta G^{\circ}\) (and hence \(K_{\mathrm{a}}\) of the acid)? (c) What processes contribute to \(\Delta H^{\circ} ?\) (Consider the ionization of the acids as a Brønsted acid-base reaction.) (d) Explain why the \(T \Delta S^{\circ}\) term is more negative for \(\mathrm{CH}_{3} \mathrm{COOH}\)
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