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Chapter 18: Problem 59

Use the following data to determine the normal boiling point, in kelvins, of mercury. What assumptions must you make in order to do the calculation? $$ \begin{aligned} \mathrm{Hg}(l): & \Delta H_{\mathrm{f}}^{\circ} &=0 \text { (by definition) } \\\ & S^{\circ} &=77.4 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol} \\ \mathrm{Hg}(g): & \Delta H_{\mathrm{f}}^{\circ} &=60.78 \mathrm{~kJ} / \mathrm{mol} \\ & S^{\circ} &=174.7 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol} \end{aligned} $$

Short Answer

Expert verified
The normal boiling point of mercury is 625 K.

Step by step solution

01

Understand Required Assumptions

In order to carry out this calculation, the primary assumption is that the boiling process is at normal pressure, which is 1 atmosphere. The second assumption is that the boiling process is in equilibrium, meaning that \(\Delta G^\circ\) is equal to zero.
02

Apply Gibbs Free Energy Equation for Phase Transition

We know that at equilibrium, \(\Delta G^\circ = 0\) (Gibbs free energy change). So, from \(\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ\), We get that \(T = \(\Delta H^\circ/\Delta S^\circ\). Here, \(\Delta H^\circ\) represents the change in enthalpy, which is the heat of vaporization, \(\Delta H_{vap}^\circ\), and \(\Delta S^\circ\) is the change in entropy due to vaporization, \(\Delta S_{vap}^\circ\). Note that these are standard conditions values, indicated by superscript \(\circ\).
03

Calculate Change in Enthalpy and Entropy

\(\Delta H_{vap}^\circ\) is given by \(\Delta H_{f(g)}^\circ - \Delta H_{f(l)}^\circ\) which is \(60.78 kJ/mol - 0 = 60.78 kJ/mol\). Similarly, \(\Delta S_{vap}^\circ\) is given by \(\Delta S_{f(g)}^\circ - \Delta S_{f(l)}^\circ\) which is \(174.7 J/K \cdot mol - 77.4 J/K \cdot mol = 97.3 J/K \cdot mol\).
04

Calculate Normal Boiling Point

Finally, we substitute the calculated values into the equation obtained in Step 2 to find the boiling temperature \(T\). Thus, \(T = \Delta H_{vap}^\circ/\Delta S_{vap}^\circ = 60.78 kJ/mol / 97.3 J/K \cdot mol = 625 K\). Remember to change the unit of enthalpy to J/mol for consistency before doing the calculation.

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Most popular questions from this chapter

State the second law of thermodynamics in words and express it mathematically.

Consider two carboxylic acids (acids that contain the \(-\mathrm{COOH}\) group \(): \mathrm{CH}_{3} \mathrm{COOH}\) (acetic acid, \(K_{\mathrm{a}}=1.8 \times 10^{-5}\) ) 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: 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 Bronsted acid-base reaction.) (d) Explain why the \(T \Delta S^{\circ}\) term is more negative for \(\mathrm{CH}_{3} \mathrm{COOH}\).

Large quantities of hydrogen are needed for the synthesis of ammonia. One preparation of hydrogen involves the reaction between carbon monoxide and steam at \(300^{\circ} \mathrm{C}\) in the presence of a copper-zinc catalyst: $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) $$.

Give a detailed example of each of the following, with an explanation: (a) a thermodynamically spontaneous process; (b) a process that would violate the first law of thermodynamics; (c) a process that would violate the second law of thermodynamics; (d) an irreversible process; (e) an equilibrium process.

How does the entropy of a system change for each of the following processes? (a) A solid melts. (b) A liquid freezes. (c) A liquid boils. (d) A vapor is converted to a solid. (e) A vapor condenses to a liquid. (f) A solid sublimes. (g) Urea dissolves in water.
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