Question

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 \(\mathrm{CH}_{3} \mathrm{COOH}\).

Short answer

The enthalpy term, ΔH°, is dominant in determining the ΔG° and thus the acidity of the acid. The process of bond breaking and formation during ionization contributes to ΔH°. The TΔS° term is more negative for CH3COOH due to better solvation of the resulting ions.

Step-by-step solution

Calculate ΔG° using Ka

Firstly, calculate ΔG° for ionization of both acids using the given Ka values and the relationship ΔG° = -RTlnKa. Here, R is the gas constant (8.314 J/K⋅mol) and T is the absolute temperature in Kelvin, in this case 298K. Remember to convert Ka values to natural log scale and keep your units consistent throughout the calculation.

Identify dominant term in ΔG°

To find out the dominant term in determining the ΔG° (and hence Ka of the acid), it might be useful to calculate ΔH° - TΔS° values for both acids and compare the resultant ΔG° values with the computed ΔG° from Step 1. The closeness of ΔH° and ΔG° values for both acids indicates the dominance of ΔH° in determining ΔG°.

Interpret ΔH° contribution

The contributions to ΔH° come from bond breaking and bond forming during the ionization. In this case, when the acid donates a proton to water (acting as a Bronsted base), the O-H bond in the acid breaks and a new O-H bond in the hydronium ion forms. Thus, ΔH° is primarily determined by the bond energies involved in these processes.

Explain the ΔS° term

Entropy, ΔS°, governs the disorder or randomness of a system. The TΔS° term in the Gibbs Free Energy equation accounts for the contribution of entropy to the overall reaction. The larger the gas molecules produced during the reaction, the more disorder (higher entropy). Since no gases are produced during the ionization of carboxylic acids, it's more likely related to the solvation of the resulting ions. The CH3COOH molecule might experience better solvation than CH2ClCOOH because CH3COOH can form stronger interactions with water, leading to a more negative ΔS° and hence a more negative TΔS° term.

Key concepts

Gibbs Free Energy

Gibbs free energy, denoted as \(\Delta G^\circ\), is a thermodynamic property that can be used to predict the direction of a chemical reaction and to gauge the reaction's spontaneity at constant temperature and pressure. The lower the value of \(\Delta G^\circ\), the more likely a reaction is to occur spontaneously.

\(\Delta G^\circ\) is given by the equation \(\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ\), where \(\Delta H^\circ\) represents the change in enthalpy, T is the temperature in Kelvin, and \(\Delta S^\circ\) is the change in entropy. For the ionization of carboxylic acids, a negative value of \(\Delta G^\circ\) implies a favorable ionization process. In our exercise, the relationship between the Gibbs free energy and the acid dissociation constant (\(K_a\)) is explored through the formula \(\Delta G^\circ = -RT\ln{K_a}\), where R is the universal gas constant. This formula allows us to calculate the \(\Delta G^\circ\) for the ionization of acetic acid and chloroacetic acid, facilitating a deeper understanding of their dissociation behaviors in an aqueous solution.

Acid Dissociation Constant (Ka)

The acid dissociation constant, known as \(K_a\), is a crucial concept in understanding the strength of an acid. It measures the degree to which an acid can donate a proton in an aqueous solution, indicative of its ionization propensity. The higher the \(K_a\) value, the stronger the acid, because a larger fraction of the acid molecules donate protons to become ions.

A carboxylic acid's \(K_a\) reflects the equilibrium concentrations of reactants and products in its ionization equation. Carboxylic acids typically have relatively small \(K_a\) values, meaning they are weak acids and do not ionize completely in water. Nonetheless, some structural differences, like the presence of electronegative atoms, can increase the acidity and thus the \(K_a\). In our exercise, for instance, chloroacetic acid has a higher \(K_a\) than acetic acid, hinting at a greater tendency to lose a proton and ionize due to the electron-withdrawing effect of the chlorine atom.

Enthalpy (Delta H)

Enthalpy, symbolized as \(\Delta H^\circ\), is a measure of the total heat content in a chemical system during a constant pressure process. It is concerned with the heat absorbed or released, depending on whether the reaction is endothermic or exothermic, respectively.

Bond Energies and Ionization

During the ionization of carboxylic acids, \(\Delta H^\circ\) entails the energy changes due to bond breaking and forming. The process involves disruption of the O-H bond in the carboxylic acid and subsequent formation of a new bond in the hydronium ion. For the acids we are considering, any difference in their \(\Delta H^\circ\) values arises from the dissimilarities in their molecular structures, and hence, the energy required to break specific bonds. The comparison of \(\Delta H^\circ\) to \(\Delta G^\circ\) indicates the extent to which enthalpy influences the ionization process.

Entropy (Delta S)

Entropy, denoted as \(\Delta S^\circ\), is a fundamental thermodynamic quantity representing the disorder or randomness within a system. Changes in entropy reflect the differences in distribution and energy levels of particles between the initial and final states of a reaction.

Entropy and Solvation

For carboxylic acids ionization, the \(\Delta S^\circ\) term is pivotal because it captures the change in disorder when an acid dissociates into ions. The solvation of ions plays a significant role here; ions are surrounded by solvent molecules, which increases system disorder. The larger the number of solvated ions, the greater the entropy. In the context of our exercise, acetic acid's \(T\Delta S^\circ\) term is more negative as compared to that of chloroacetic acid, suggesting that upon ionization, the resulting ions from acetic acid result in a higher state of disorder, likely due to stronger interactions with water molecules that enhance solvation and therefore contribute to a higher \(\Delta S^\circ\).