Passage
Students conducted an experiment to determine the changes in enthalpy ΔH°, entropy ΔS°, and Gibbs free energy ΔG° resulting from the dissociation of acetic acid (CH₃COOH) in water. The students first determined the acid dissociation constant K_a for the reaction by measuring the pH of a 1 M acetic acid solution at various temperatures over a narrow range of less than 10 °C.To perform the pH measurements, the acetic acid solution was initially cooled to 0 °C using an ice bath and then warmed with gentle heating to room temperature with continuous stirring. The pH was recorded at intervals of 1 °C. From the pH data, the value of K_a at each temperature T was calculated. The experimental results over the selected temperature range are shown in Table 1.Table 1 Student Data for the pH and K_a of Acetic Acid with Increasing Temperature
To evaluate ΔH° and ΔS°, the students constructed a van 't Hoff plot (Figure 1) , which is a graph of the natural log of the dissociation constant (ln K_a) vs. the reciprocal absolute temperature (1/T) .
Figure 1 Linear van 't Hoff plot relating the dissociation constant K_a of acetic acid to temperature TThe relationship between K_a, T, ΔH°, and ΔS° in the van 't Hoff plot was then described using a linear fit of the data following the form of Equation 1, in which R is the gas constant (8.3 J∙mol⁻¹∙K⁻¹) .
Adapted from: C. Rezsnyak "Determination of Thermodynamic Values (S°, H°, and G°) from the Dissociation of a Weak Acid" World Journal of Chemical Education. ©2017 Science and Education Publishing.
-According to the experimental results in the passage, the dissociation of acetic acid is:spontaneous at all temperatures.nonspontaneous at low temperatures.spontaneous at high temperatures.

Question

Passage
Students conducted an experiment to determine the changes in enthalpy ΔH°, entropy ΔS°, and Gibbs free energy ΔG° resulting from the dissociation of acetic acid (CH₃COOH) in water. The students first determined the acid dissociation constant K_a for the reaction by measuring the pH of a 1 M acetic acid solution at various temperatures over a narrow range of less than 10 °C.To perform the pH measurements, the acetic acid solution was initially cooled to 0 °C using an ice bath and then warmed with gentle heating to room temperature with continuous stirring. The pH was recorded at intervals of 1 °C. From the pH data, the value of K_a at each temperature T was calculated. The experimental results over the selected temperature range are shown in Table 1.Table 1 Student Data for the pH and K_a of Acetic Acid with Increasing Temperature

To evaluate ΔH° and ΔS°, the students constructed a van 't Hoff plot (Figure 1) , which is a graph of the natural log of the dissociation constant (ln K_a) vs. the reciprocal absolute temperature (1/T) .

Figure 1 Linear van 't Hoff plot relating the dissociation constant K_a of acetic acid to temperature TThe relationship between K_a, T, ΔH°, and ΔS° in the van 't Hoff plot was then described using a linear fit of the data following the form of Equation 1, in which R is the gas constant (8.3 J∙mol⁻¹∙K⁻¹) .

Adapted from: C. Rezsnyak "Determination of Thermodynamic Values (S°, H°, and G°) from the Dissociation of a Weak Acid" World Journal of Chemical Education. ©2017 Science and Education Publishing.
-According to the experimental results in the passage, the dissociation of acetic acid is:spontaneous at all temperatures.nonspontaneous at low temperatures.spontaneous at high temperatures.

Quizplus · Accepted Answer

11ecba2d_122d_aa8b_a3bf_1d66471461ff_MD0008_00 A process, such as a chemical reaction or a phase change, is spontaneous if it does not require a continuous input of additional energy to occur. According to the second law of thermodynamics, a spontaneous process in an isolated system is irreversible and always results in a net increase in overall entropy (ΔS°_overall): 11ecba2d_122d_aa8c_a3bf_a53b8ab85fc1_MD0008_00 Because the entropy of the surroundings cannot be calculated, the spontaneity (or nonspontaneity) of a process is instead evaluated using the change in Gibbs free energy ΔG °, which is related to the changes in enthalpy ΔH °, entropy ΔS °, and temperature T of the system by 11ecba2d_122d_aa8d_a3bf_6b2aa8976bde_MD0008_00 Accordingly, when ΔG ° < 0, the reaction is spontaneous because the products have less free energy than the reactants. When ΔG ° > 0, the reaction is nonspontaneous because the products have more free energy than the reactants. When ΔG ° = 0, the reaction is already at its lowest energy state at equilibrium. This means one of four possible outcomes can occur: When ΔS ° is positive and ΔH ° is negative, the process is always spontaneous (−ΔG °). When ΔS ° is negative and ΔH ° is positive, the process is not spontaneous (+ΔG °) at any temperature. When both ΔS ° and ΔH ° are negative, the process is spontaneous (−ΔG °) at low temperatures and nonspontaneous (+ΔG °) at high temperatures (ie, an exothermic reaction). When both ΔS ° and ΔH ° are positive, the process is spontaneous (−ΔG °) at high temperatures and nonspontaneous (+ΔG °) at low temperatures (ie, an endothermic reaction). Based on the experiment in the passage, ΔH ° is positive and ΔS ° is positive; therefore, the reaction is nonspontaneous at low temperatures (Number II) but spontaneous at high temperatures (Number III). As such, the reaction is endothermic and is not spontaneous at all temperatures (Number I). Educational objective: A spontaneous process does not require a continuous input of additional energy. The change in Gibbs free energy (ΔG °) is evaluated as ΔG ° = ΔH ° − TΔS ° and is used to identify whether a process is spontaneous (ΔG ° ˂ 0), nonspontaneous (ΔG ° > 0), or at equilibrium (ΔG ° = 0). Processes in which both changes in entropy ΔS ° and enthalpy ΔH ° are positive are spontaneous at high temperatures and nonspontaneous at low temperatures.

Passage Students Conducted an Experiment to Determine the Changes in Enthalpy