Passage Students Conducted an Experiment to Determine the Changes in Enthalpy

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?

A) 4911R−T(5.4R)
B) 5.4R+T(4911R)
C)
D)

Correct Answer:

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