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.
-The slope of the trendline for the data in Figure 1 is −4911 and its y-intercept is 5.4. Which of the following is an expression for ΔG° at temperature T stated in terms of the data?

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.
-The slope of the trendline for the data in Figure 1 is −4911 and its y-intercept is 5.4. Which of the following is an expression for ΔG° at temperature T stated in terms of the data?

Quizplus · Accepted Answer

11ecba2d_122c_c022_a3bf_ef5ba680bd24_MD0008_00 The change in Gibbs free energy ΔG° for a reaction is related to the changes in enthalpy ΔH° and entropy ΔS° at temperature T (measured in Kelvin) by the formula 11ecba2d_122c_c023_a3bf_8b5d2bfafc6a_MD0008_00 In the equation above, the degree symbol indicates that all thermodynamic values are reported in standard state at equilibrium for a process in which the reactants have a concentration of 1 M. Although ΔH° describes the flow of heat in a reaction and ΔS° describes the disorder of the products relative to the reactants, ΔG° does not have a physical correlation. Rather, ΔG° is a state function that describes the spontaneity of the reaction (ie, its likelihood to occur without additional intervention). In a van 't Hoff plot, the enthalpy and entropy of a reaction can be found from the slope and the y-intercept of the trendline, respectively. In this experiment, the slope of the trendline is −4911. According to the linear fit of the data (Equation 1), the slope is equal to 11ecba2d_122c_c024_a3bf_9f9ee1118706_MD0008_00 Using this relationship and solving for ΔH° gives: 11ecba2d_122c_c025_a3bf_a9dc6332b7d1_MD0008_00 11ecba2d_122c_c026_a3bf_e11cdb961597_MD0008_00 Similarly, setting the y-intercept value of 5.4 equal to the y-intercept term 11ecba2d_122c_e737_a3bf_eb41e2f9a5b8_MD0008_00 from Equation 1 and solving for ΔS° gives: 11ecba2d_122c_e738_a3bf_c31efd97342e_MD0008_00 11ecba2d_122c_e739_a3bf_3f8bd8ea373c_MD0008_00 Substituting the expressions for ΔH° and ΔS° above into the equation for Gibbs free energy yields: 11ecba2d_122c_e73a_a3bf_6f2aba5ba2f2_MD0008_00 (Choice B) This is the answer obtained when ΔS° and ΔH° are switched in the Gibbs free energy equation. (Choice C) This is the answer obtained if the terms for the slope and the y-intercept (−4911/R and 5.4/R) from Equation 1 are substituted into the Gibbs free energy equation without first solving the respective terms for ΔH° and ΔS°. (Choice D) This is the answer obtained by mixing up the substitution of the terms for the slope and the y-intercept from Equation 1 into the Gibbs free energy equation and failing to first solve the respective terms for ΔH° and ΔS°. Educational objective: The Gibbs free energy is a state function that describes the spontaneity of a reaction. It is related to the temperature, enthalpy, and entropy of the reaction via the equation ΔG° = ΔH° − TΔS°, where T is given in Kelvin.

Passage Students Conducted an Experiment to Determine the Changes in Enthalpy