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Chapter 19: Problem 103

Most liquids follow Trouton's rule (see Exercise 19.93 ), which states that the molar entropy of vaporization is approximately $88 \pm 5 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows: \begin{tabular}{lcc} \hline & Normal Boiling & \\ Substance & Point \(\left({ }^{\circ} \mathrm{C}\right)\) & $\Delta H_{\text {vap }}(\mathrm{k} / / \mathrm{mol})$ \\ \hline Acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}\) & 56.1 & 29.1 \\\ Dimethyl ether, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{O}\) & -24.8 & 21.5 \\\ Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) & 78.4 & 38.6 \\ Octane, \(\mathrm{C}_{\mathrm{s}} \mathrm{H}_{18}\) & 125.6 & 34.4 \\ Pyridine, \(\mathrm{C}_{5} \mathrm{H}_{\mathrm{S}} \mathrm{N}\) & 115.3 & 35.1 \\\ \hline \end{tabular} (a) Calculate \(\Delta S_{\text {vap }}\) for each of the liquids. Do all the liquids obey Trouton's rule? (b) With reference to intermolecular forces (Section 11.2), can you explain any exceptions to the rule? (c) Would you expect water to obey Trouton's rule? By using data in Appendix \(\mathrm{B}\), check the accuracy of your conclusion. (d) Chlorobenzene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\right)\) boils at \(131.8^{\circ} \mathrm{C}\). Use Trouton's rule to estimate $\Delta H_{\text {vap }}$ for this substance.

Short Answer

Expert verified
In this exercise, the molar entropy of vaporization (\(\Delta S_{vap}\)) was calculated for various organic liquids. Comparing the calculated values to Trouton's rule, it was found that not all the liquids obey the rule, with ethanol being an exception due to stronger hydrogen bonding. Water also doesn't follow Trouton's rule because of its strong hydrogen bonding network, resulting in a higher \(\Delta S_{vap}\) value. For chlorobenzene, assuming it follows Trouton's rule, its estimated enthalpy of vaporization is approximately 35.63 kJ/mol.

Step by step solution

01

Part (a): Calculate \(\Delta S_{vap}\) for each liquid

To calculate the molar entropy of vaporization \(\Delta S_{vap}\) for each liquid, we'll use the formula: \[\Delta S_{vap} = \frac{\Delta H_{vap}}{T_b}\] where \(\Delta H_{vap}\) is the enthalpy of vaporization, and \(T_b\) is the normal boiling point in Kelvin. First, let's convert the boiling points from Celsius to Kelvin: \[T_b(K) = T_b(^{\circ}C) + 273.15\] For each liquid, calculate the entropy of vaporization and check if it follows Trouton's rule: 1. Acetone: \[T_b = 56.1 + 273.15 = 329.25 \mathrm{~K}\] \[\Delta S_{\text{vap}} = \frac{29.1 * 10^3}{329.25} = 88.34 \mathrm{~J/mol~K}\] 2. Dimethyl Ether: \[T_b = -24.8 + 273.15 = 248.35 \mathrm{~K}\] \[\Delta S_{\text{vap}} = \frac{21.5 * 10^3}{248.35} = 86.54 \mathrm{~J/mol~K}\] 3. Ethanol: \[T_b = 78.4 + 273.15 = 351.55 \mathrm{~K}\] \[\Delta S_{\text{vap}} = \frac{38.6 * 10^3}{351.55} = 109.69 \mathrm{~J/mol~K}\] 4. Octane: \[T_b = 125.6 + 273.15 = 398.75 \mathrm{~K}\] \[\Delta S_{\text{vap}} = \frac{34.4 * 10^3}{398.75} = 86.26 \mathrm{~J/mol~K}\] 5. Pyridine: \[T_b = 115.3 + 273.15 = 388.45 \mathrm{~K}\] \[\Delta S_{\text{vap}} = \frac{35.1 * 10^3}{388.45} = 90.33 \mathrm{~J/mol~K}\] Comparing the calculated \(\Delta S_{\text{vap}}\) values to Trouton's rule limits (88 ± 5 J/mol K), we can observe that not all the liquids obey the rule. Ethanol is the exception with a higher entropy of vaporization than the expected range.
02

Part (b): Intermolecular forces and exceptions to Trouton's rule

Ethanol doesn't obey Trouton's rule due to the presence of hydrogen bonding, which is a stronger intermolecular force than van der Waals forces experienced by other organic liquids. This hydrogen bonding increases the energy required for vaporization, leading to a higher molar entropy of vaporization.
03

Part (c): Water and Trouton's rule

We would not expect water to obey Trouton's rule since it has a very strong hydrogen bonding network, which would result in a higher molar entropy of vaporization than predicted by the rule. Using data from Appendix B: \[T_b = 100^{\circ} C \Rightarrow 373.15 \mathrm{~K}\] \[\Delta H_{\text{vap}} = 40.7 \mathrm{~kJ/mol}\] Calculate \(\Delta S_{\text{vap}}\) for water: \[\Delta S_{\text{vap}} = \frac{40.7 * 10^3}{373.15} = 109.07 \mathrm{~J/mol~K}\] As expected, the \(\Delta S_{\text{vap}}\) value for water (109.07 J/mol K) doesn't obey Trouton's rule due to its strong hydrogen bonding network.
04

Part (d): Estimate \(\Delta H_{vap}\) for Chlorobenzene using Trouton's rule

According to Trouton's rule, we can estimate the molar entropy of vaporization \(\Delta S_{\text{vap}}\) to be 88 J/mol K (assuming it follows the rule). We are given the boiling point of chlorobenzene: \[T_b = 131.8^{\circ} C \Rightarrow 404.95 \mathrm{~K}\] Using the estimated \(\Delta S_{\text{vap}}\) and the boiling point, we can calculate \(\Delta H_{\text{vap}}\): \[\Delta H_{\text{vap}} = \Delta S_{\text{vap}} * T_b\] \[\Delta H_{\text{vap}} = 88 * 404.95 \approx 35.63 \mathrm{~kJ/mol}\] So, the estimated enthalpy of vaporization for chlorobenzene is approximately 35.63 kJ/mol using Trouton's rule.

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Most popular questions from this chapter

When most elastomeric polymers (e.g., a rubber band) are stretched, the molecules become more ordered, as illustrated here: Suppose you stretch a rubber band. (a) Do you expect the entropy of the system to increase or decrease? (b) If the rubber band were stretched isothermally, would heat need to be absorbed or emitted to maintain constant temperature? (c) Try this experiment: Stretch a rubber band and wait a moment. Then place the stretched rubber band on your upper lip, and let it return suddenly to its unstretched state (remember to keep holding on!). What do you observe? Are your observations consistent with your answer to part (b)?

The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$, is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: $$ 2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g) $$ In practice, this reaction is carried out in the presence of oxygen: $$ 2 \mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ (a) Using the data in Appendix \(C\), calculate \(K\) for these reactions at \(25^{\circ} \mathrm{C}\) and \(500^{\circ} \mathrm{C}\). (b) Is the difference in \(\Delta G^{\circ}\) for the two reactions due primarily to the enthalpy term \((\Delta H)\) or the entropy term \((-T \Delta S)\) ? (c) Explain how the preceding reactions are an example of driving a nonspontaneous reaction, as discussed in the "Chemistry and Life" box in Section 19.7. (d) The reaction of \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) to form \(\mathrm{C}_{2} \mathrm{H}_{6}\) and \(\mathrm{H}_{2} \mathrm{O}\) must be carried out carefully to avoid a competing reaction. What is the most likely competing reaction?

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which 3 mol of gaseous reactants are converted to 2 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

Indicate whether \(\Delta G\) increases, decreases, or does not change when the partial pressure of \(\mathrm{H}_{2}\) is increased in each of the following reactions: (a) $\mathrm{H}_{2}(g)+\mathrm{NiO}(s) \longrightarrow \mathrm{Ni}(s)+\mathrm{H}_{2} \mathrm{O}(g)$ (b) $\mathrm{H}_{2}(g)+\mathrm{S}(s) \longrightarrow \mathrm{H}_{2} \mathrm{~S}(g)$ (c) $\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)$

(a) Which of the thermodynamic quantities \(p, H, q, w,\) and \(G\) are state functions? (b) Consider a system going from state 1 to state 2 in a reversible and an irreversible way. Compare \(q_{\text {rev }}\) and \(q_{\text {irtev }}\) (c) Consider a system going from state 1 to state 2 in a reversible and an irreversible way. Compare \(w_{\text {rev }}\) and \(w_{\text {trev }}\). (d) For a reversible isothermal process, write an expression for \(\Delta H\) and an expression for \(\Delta G\) in terms of \(q, w\) and \(T, p\) and \(\Delta V\).
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