Most liquids follow Trouton's rule, which states that the...

Most liquids follow Trouton's rule, which states that the molar entropy of vaporization lies in the range of $88 \pm 5 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows: $$ \begin{array}{lrl} \hline \text { Substance } & \begin{array}{l} \text { Normal Boiling } \\ \text { Point }\left({ }^{\circ} \mathrm{C}\right) \end{array} & \begin{array}{l} \Delta H_{\text {vap }} \\ \text { (kJ/mol) } \end{array} \\ \hline \text { Acetone, }\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO} & 56.1 & 29.1 \\ \text { Dimethyl ether, }\left(\mathrm{CH}_{3}\right)_{2} \mathrm{O} & -24.8 & 21.5 \\ \text { Ethanol } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} & 78.4 & 38.6 \\ \text { Octane, } \mathrm{C}_{8} \mathrm{H}_{18} & 125.6 & 34.4 \\ \text { Pyridine, } \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N} & 115.3 & 35.1 \\ \hline \end{array} $$ (a) Calculate $\Delta \mathrm{S}_{\mathrm{vap}}$ for each of the liquids. Do all of 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.

Most liquids follow Trouton's rule, which states that the molar entropy of vaporization lies in the range of $88 \pm 5 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows:
$$
\begin{array}{lrl}
\hline \text { Substance } & \begin{array}{l}
\text { Normal Boiling } \\
\text { Point }\left({ }^{\circ} \mathrm{C}\right)
\end{array} & \begin{array}{l}
\Delta H_{\text {vap }} \\
\text { (kJ/mol) }
\end{array} \\
\hline \text { Acetone, }\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO} & 56.1 & 29.1 \\
\text { Dimethyl ether, }\left(\mathrm{CH}_{3}\right)_{2} \mathrm{O} & -24.8 & 21.5 \\
\text { Ethanol } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} & 78.4 & 38.6 \\
\text { Octane, } \mathrm{C}_{8} \mathrm{H}_{18} & 125.6 & 34.4 \\
\text { Pyridine, } \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N} & 115.3 & 35.1 \\
\hline
\end{array}
$$ (a) Calculate $\Delta \mathrm{S}_{\mathrm{vap}}$ for each of the liquids. Do all of 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.

Key Concepts

Hydrogen Bonding and Exceptions

Hydrogen bonding is a specific, strong type of dipole-dipole interaction that can substantially alter the thermodynamic behavior of a substance. Molecules that engage in hydrogen bonding, such as water and alcohols, often have higher enthalpies of vaporization and lower entropies of vaporization than predicted by Trouton's rule because the orderly hydrogen bond network in the liquid phase requires additional energy to disrupt. This effect is a primary reason for deviations from the rule in such cases.

Estimations Using Trouton's Rule

Trouton's rule is frequently used to estimate unknown enthalpies of vaporization by assuming a typical molar entropy of vaporization value. For example, if the boiling point of a substance is known, one can approximate ?Hvap by multiplying the boiling temperature in Kelvin by the average ?Svap value (?88 J/mol·K). This estimation method provides a quick, approximate calculation of the energy required for vaporization, although it may not be accurate for substances with significant deviations due to specific intermolecular forces.

Intermolecular Forces

Intermolecular forces, such as van der Waals interactions, dipole-dipole interactions, and hydrogen bonds, play a key role in determining the physical properties of liquids, including their boiling points, enthalpies, and entropies of vaporization. Variations in these forces can lead to deviations from empirical rules like Trouton's rule, as liquids with unusually strong or directional interactions may exhibit significantly different thermodynamic properties.

Entropy of Vaporization

The entropy of vaporization (?Svap) quantifies the increase in disorder when a liquid is converted into its vapor. It is calculated using the relationship ?Svap = ?Hvap/Tb, where ?Hvap is the enthalpy of vaporization and Tb is the normal boiling temperature in Kelvin. This concept is central to understanding the molecular changes and energy dispersal that occur during the phase transition.

Enthalpy of Vaporization

The enthalpy of vaporization (?Hvap) is the amount of energy required to convert one mole of a liquid into vapor at its boiling point under standard pressure. It reflects the strength of intermolecular forces within the liquid; stronger forces necessitate a higher ?Hvap. This parameter is crucial for analyzing phase changes and for various applications in chemical and process engineering.

Trouton's Rule

Trouton's rule is an empirical observation in thermodynamics which notes that many liquids exhibit a nearly constant molar entropy of vaporization at their normal boiling points, typically around 88 ± 5 J/mol·K. This rule provides a useful approximation for the entropy change associated with vaporization and is often applied for liquids that do not engage in particularly strong intermolecular interactions.

Transcript

00:01 Acetic acid can be manufacturing by combining methanol with carbon dioxide in a carbonylation reaction.

00:11 Here is an example.

00:17 I should say the reaction.

00:36 We are asked a to calculate the equilibrium constant for this reaction.

00:50 Okay.

00:55 We can use this equation.

01:18 So we can find our delta g by using our free energy change by using the free energy values of products and reactants.

01:28 I'm drinking coffee, excuse me.

02:01 We can look these up in appendix c.

02:06 So for the given reaction, our delta g can be calculated as follows.

02:19 Let me just write down there.

02:52 Next, we can put this into the equation we listed at the beginning.

03:39 So there is our k.

03:42 That is our equilibrium constant.

03:49 B, industrial speaking, this reaction is run above.

03:55 25 degrees celsius.

04:04 With an increased will an increase in temperature produce an increase or decrease in the bulk fraction of acetic acid and why are elevated temperatures used.

05:14 Okay the reaction is exothermic.

05:19 So let's go ahead and do our delta h calculations which is just like delta g instead of the delta g's where you gonna use our delta hs.

05:27 So it's gonna be products minus reactants.

05:31 These are values we look up in the text...

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