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Chapter 17: Problem 57

Consider the following Brønstead acid-base reaction at \(25^{\circ} \mathrm{C}\) : $$ \mathrm{HF}(a q)+\mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{HCl}(a q)+\mathrm{F}^{-}(a q) $$ (a) Predict whether \(K\) will be greater or smaller than unity. (b) Does \(\Delta S^{\circ}\) or \(\Delta H^{\circ}\) make a greater contribution to \(\Delta G^{\circ} ?\) (c) Is \(\Delta H^{\circ}\) likely to be positive or negative?

Short Answer

Expert verified
(a) The value of K is likely to be around unity. (b) The enthalpy change (\(\Delta H^{\circ}\)) likely makes a greater contribution to the free energy change (\(\Delta G^{\circ}\)) than the entropy change (\(\Delta S^{\circ}\)). (c) \(\Delta H^{\circ}\) is likely to be positive, suggesting that the reaction is endothermic.

Step by step solution

01

Predict the equilibrium constant

The equilibrium constant (K) confers the ratio of product concentration over reactant concentration at equilibrium. In this reaction, there are equal number of species on both sides. Hence, it is expected that K will be around unity.
02

Determine the dominant contributor to the free energy change

The free energy change (\(\Delta G^{\circ}\)) of a system can be calculated using the equation: \(\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\). Since the temperatures for this reaction are fairly modest (at 25°C) and there is no net change in molar gas quantity in the reaction, the enthalpy change (\(\Delta H^{\circ}\)) likely makes the greater contribution to \(\Delta G^{\circ}\).
03

Predict the sign of \(\Delta H^{\circ}\)

In order to determine whether \(\Delta H^{\circ}\) is positive or negative, one can look at the strength of the bonds being broken and formed during the reaction. Stronger bonds have lower bond energy, so breaking them requires more energy (endothermic - positive \(\Delta H^{\circ}\)), while forming them releases energy (exothermic - negative \(\Delta H^{\circ}\)). In this case, the HF bond is known to be stronger than the HCl bond that's being formed, so more energy is likely spent on breaking bonds than is released when new bonds are formed. As such, the reaction is likely endothermic with a positive \(\Delta H^{\circ}\).

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Most popular questions from this chapter

For the autoionization of water at \(25^{\circ} \mathrm{C}\), $$ \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ \(K_{\mathrm{w}}\) is \(1.0 \times 10^{-14} .\) What is \(\Delta G^{\circ}\) for the process?

Which of the following processes are spontaneous and which are nonspontaneous at a given temperature? (a) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q) \quad\) saturated soln (b) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q) \quad\) unsaturated soln (c) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q)\) supersaturated soln

In the metabolism of glucose, the first step is the conversion of glucose to glucose 6 -phosphate: glucose \(+\mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow\) glucose 6 -phosphate \(+\mathrm{H}_{2} \mathrm{O}\) $$ \Delta G^{\circ}=13.4 \mathrm{~kJ} / \mathrm{mol} $$ Because \(\Delta G^{\circ}\) is positive, this reaction does not favor the formation of products. Show how this reaction can be made to proceed by coupling it with the hydrolysis of ATP. Write an equation for the coupled reaction and estimate the equilibrium constant for the coupled process.

Which of the following is not accompanied by an increase in the entropy of the system: (a) mixing of two gases at the same temperature and pressure, (b) mixing of ethanol and water, (c) discharging a battery, (d) expansion of a gas followed by compression to its original temperature, pressure, and volume?

What is a coupled reaction? What is its importance in biological reactions?
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