Acid Ionization Reactions: A Capstone Multiconcept Thermodynamics

Apr 12, 2013 - application of Hess,s law; NaOH(aq) is the base. A datalogger and a temperature sensor (±0.01 °C sensitivity) are used to measure and...
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The H3PO4 Acid Ionization Reactions: A Capstone Multiconcept Thermodynamics General Chemistry Laboratory Exercise Frazier Nyasulu,* Rebecca Barlag, Lindy Wise, and Lauren McMills Department of Chemistry and Biochemistry, Ohio University, Athens, Ohio 45701, United States S Supporting Information *

ABSTRACT: The thermodynamic properties of weak acid ionization reactions are determined. The thermodynamic properties are corresponding values of the absolute temperature (T), the weak acid equilibrium constant (Ka), the enthalpy of ionization (ΔiH°), and the entropy of ionization (ΔiS°). The enthalpy of ionization (ΔiH°) is determined from the enthalpy of neutralization of HCl(aq) and the enthalpy of neutralization of the weak acid by application of Hess’s law; NaOH(aq) is the base. A datalogger and a temperature sensor (±0.01 °C sensitivity) are used to measure and plot the thermograms of the reactions. The calorimeter constant (CCal) is determined by electrical heating of the post-reaction solution; procedure takes 10−20 s for each CCal determination. With NaOH(aq) as the limiting reagent, the post-reaction solutions consist of a weak acid and corresponding conjugate base allowing Ka to be determined from the measured pH of these solutions. The values of T, Ka, and ΔiH° are used to calculate ΔiS° according to the equation: ΔiG° = −RT ln Ka = ΔiH° − TΔiS°. The choice of H3PO4(aq), a triprotic weak acid, provides an opportunity for students to predict and explain expected trends in Ka, ΔiH°, and ΔiS° prior to their determination. The multiconcept nature of this lab exercise makes it an ideal capstone laboratory exercise in general chemistry. KEYWORDS: First-Year Undergraduate/General, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Acids/Bases, Aqueous Solution Chemistry, Calorimetry/Thermochemistry, Equilibrium, pH, Solutions/Solvents

A

In choosing a weak acid ionization reaction, the standard enthalpy of reaction is the standard enthalpy of ionization (ΔiH°) and the equilibrium constant is the acid ionization constant (Ka). ΔiH° is determined from enthalpies of neutralization of the weak acid and the enthalpy of neutralization of a strong acid by application of Hess’s law. This exercise provides an opportunity for students to review the determination of enthalpy of neutralization and the determination of a weak acid ionization constant. Students are also introduced to the electrical determination of the calorimeter constant using a procedure that accentuates the data recording and data analysis abilities of the modern datalogger and temperature sensor. The experiment consists of three parts: (i) determination of the temperature change upon adding NaOH to the acid solution, where NaOH is the limiting reagent; (ii) electrical determination of the calorimeter constant; and (iii) measurement of the pH of the post-reaction solution, which consists of a weak acid and a corresponding conjugate base. The choice of H3PO4, a triprotic weak acid, provides an opportunity to predict, determine, and explain trends in Ka, ΔiH°, and ΔiS°. Data analysis is substantial, requiring the use of a spreadsheet.

multiconcept laboratory exercise is described in which the thermodynamics of weak acid ionization reactions are determined. It builds upon several earlier laboratory exercises, for example, the enthalpy of neutralization of a weak acid with NaOH(aq) and the determination of the weak acid ionization constant. However, this lab exercise can be used as a standalone exercise. The goal in this thermodynamics experiment is to determine corresponding values of the absolute temperature (T), equilibrium constant (K), Gibbs energy (ΔG°), standard enthalpy (ΔH°), and the standard entropy (ΔS°). These terms are interrelated by the equation: ΔG° = −RT ln K = ΔH ° − T ΔS°

(1)

The standard enthalpy (ΔH°) and standard entropy (ΔS°) can be determined in one of two approaches. In the first approach, the equilibrium constant (K) is determined as a function of absolute temperature (T). A plot of ln K versus 1/T allows ΔH° to be determined from the slope (ΔH° = −slope/R) and ΔS° to be determined from the y intercept (ΔS° = y intercept/ R).1−14 In the second approach, T, K, and ΔH° are determined, and ΔS° is calculated according to eq 1.15,16 For any given reaction, one approach may be easier or more practical to implement than the other. This exercise is based on the second approach. © 2013 American Chemical Society and Division of Chemical Education, Inc.

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Laboratory Experiment

Δi G° = −RT ln Ka1 = Δi(H3PO4 )H ° − T Δi(H3PO4 )S°

THEORY The enthalpies of ionization of H3PO4 are labeled Δi(H3PO4)H°, Δi(H2PO−4 )H°, and Δi(HPO2− H° for the first, second, and third 4 ) ionizations, respectively. Similarly, the enthalpy of neutralization of the first, second, and third acidic H+ are labeled H°, respecΔNeutr.(H3PO4)H°, ΔNeutr.(H2PO−4 )H°, and ΔNeutr.(HPO2− 4 ) tively. Δi(H3PO4)H° is determined from the enthalpy of neutralization of H3PO4(aq) and enthalpy of neutralization of HCl(aq) as indicated by the equations below. To ensure that only the first acidic H+ is involved, the amount of NaOH is typically 40−60% of the amount of H3PO4(aq). Equations 2 and 3 add to give eq 4.

(10)

Similar equations can be written for Δi(H2PO−4 )S° and Δi(HPO2− S°. 4 )

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EXPERIMENTAL DETAILS

Lab Implementation

Students work in pairs in a 3-h lab session. Each pair performs all measurements and each run is repeated four times so that an average and standard deviation can be calculated. Detailed information about how to perform the required measurements can be found in the Supporting Information. Materials and Equipment

Pasco Scientific datalogger, temperature sensor, pH sensor, dc regulated power supply (Extech Instruments), electric calorimeter (Science Lab Supplies), Styrofoam cups (3 per pair), stirrer, stir bars, stir bar retrievers, autopipettors, 10.00 M NaOH(aq, standardized), 2.0 M HCl(aq), 2.0 M H3PO4(aq), 2.0 M NaH2PO4(aq), 2.0 M K2HPO4(aq). Determination of the Temperature Change upon Adding NaOH to the Acid Solution

In accordance with Hess’s law: Δi(H3PO4 )H ° + ΔNeutr.(HCl)H ° = ΔNeutr.(H3PO4 )H °

The experimental setup is shown in Figure 1. Distilled water, aqueous acid solution (HCl, H3PO4, H2PO4−, or HPO42−) and

(5)

Similar equations can be written for Δi(H2PO4−)H° and H°. Δi(HPO2− 4 ) Electrical heating is a convenient way to determine a calorimeter constant, CCal.16 If the electrical heat energy input rate is constant, and if heat loss to the surroundings is minimal, the temperature of the calorimeter rises linearly with time. In this case: Energy Input Rate (J/s) = CCal × Slope (°C/s)

(6)

Solving for Ccal in eq 6 CCal = =

Energy Input Rate (J/s) Slope(°C/s) Voltage (J/s) × Current (C/s) Slope (°C/s)

(7) Figure 1. System setup to measure the temperature.

With NaOH(aq) as the limiting reagent, the enthalpy of neutralization is ΔNeutr.H ° = −

CCal × ΔT mol NaOH(aq)

a small stir bar are added to a Styrofoam cup. The temperature (0.01 °C sensitivity) of the stirred solution is measured at 0.5 s intervals and NaOH(aq) is added and the temperature measured for an additional 15 s. The average density of each acid is determined by measuring the mass of milliliter aliquots so that the moles of acid added to the calorimeter can be determined from the density and the mass of the acid.

(8)

where ΔT is the change in temperature upon addition of NaOH(aq) to the acid solution. Because NaOH(aq) is the limiting reagent, the post-reaction solution is a buffer solution, consisting of the weak acid and its conjugate base. The following equation is used to calculate pKa1 from the measured pH of the post-reaction buffer solution:

Electrical Determination of the Calorimeter Constant

⎛ [H PO−(aq)] ⎞ pH = pKa1 + log⎜ 2 4 ⎟ ⎝ [H3PO4 (aq)] ⎠

The calorimeter constant is determined using the post-reaction mixture and the setup shown in Figure 1. The Styrofoam cup consists of the reaction mixture and the temperature sensor (white) and the electrical heating head (red and black leads). The voltage on the dc power source is set between 3.0 and 3.8 V; both the voltage and the current are recorded. The temperature is measured at 1 s intervals; data collection lasts 10−20 s. The slope in the thermogram is determined using the data analysis tool on the datalogger.

⎞ ⎛ mol NaOH(aq) added ⎟ = pKa1 + log⎜ ⎝ initial mol H3PO4 (aq) − mol NaOH(aq) added ⎠

(9) −

Similar equations can be written for H2PO4 (aq) and HPO42−(aq) post-reaction solutions. With T, Δi(H3PO4)H°, and Ka1 values known, Δi(H3PO4)S° can be calculated according to 643

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Laboratory Experiment

Measurement of the pH of the Post-Reaction Solutions

With high linearity in the slope of the electrical heating thermogram (R2 > 0.99), 10−20 s provide 10− 20 data points, which suffice to establish the slope with sufficient certainty. The literature values for the enthalpies of ionization of H3PO4(aq) are −7.5, 3.3, and 15 kJ/mol for the first, second, and third acid ionizations, respectively.16−19 The results reported by students are within 10% of the literature values suggesting that the entire procedure, including the determination of the calorimeter constant from the heating slope, yield satisfactory results. The ΔiH°values become more positive in going from H3PO4(aq) to H2PO4−(aq) to HPO42−(aq). The process is progressively more endothermic because it is more difficult to ionize the negatively charged H2PO4−(aq) and HPO42−(aq) ions. The increasing charge magnitude on the anions, H2PO4−(aq), HPO42−(aq), and PO43−(aq) also results in greater hydration order; entropy decreases by 60− 70 J/ (K·mol) for each ionization. Whereas increasing the temperature has no effect on ΔiH° values, it does, however, make −TΔiS° values more positive, which in turn increases ΔiG° values. With ΔiG° increasing, eq 1 indicates that Ka will decrease.

The pH of each of the three weak acid−NaOH post-reaction mixtures is measured. The mixtures consist of a weak acid and a corresponding conjugate base.

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HAZARDS Sodium hydroxide is caustic and causes burns to any area of contact. Gloves should be used to handle 10.00 M NaOH(aq). Hydrochloric acid is corrosive and is hazardous in case of skin or eye contact.

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RESULTS Typical temperature changes observed upon adding NaOH(aq) to H3PO4(aq) are 2−3 °C and the electrical heating thermograms of post-reaction solutions are linear; R2 > 0.99. CCal and ΔNeutr.H° are calculated according to eq 7 and eq 8, respectively. From the pH of the post-reaction H3PO4(aq), Ka1 is calculated according to eq 9. Table 1 provides data and Table 1. Student Data and Results forΔNeutr.(H3PO4)H° Enthalpy of Neutralization a

Mass 2.0 M H3PO4(aq) added /g Amount of H3PO4(aq)/mol Initial temperature/°C Final temperature/°C Temperature change/°C Voltage/V Current/A Heating slope/(°C/s) Calorimeter constant/(J/°C) ΔNeutr.(H3PO4)H°/(kJ/mol)

Run 1

Run 2

Run 3

12.544 0.0228 22.86 25.38 2.52 3.49 2.38 0.0313 265.4 −66.8

12.274 0.0223 22.14 24.42 2.28 3.51 2.38 0.0282 296.2 −67.5

14.382 0.0261 22.04 24.53 2.49 3.48 2.39 0.0322 258.3 −64.3

Average ΔNeutr.H°/(kJ/mol) Acid Ionization Constant Run 1 Run 2 pH Ka1 a

2.06 0.00681 Average Ka1

2.11 0.00607

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SUMMARY

T, K, and ΔiH° are determined experimentally and ΔiS° is calculated according to eq 1. The three values can be determined with reasonable accuracy leading to a reliable value of ΔiS°. The choice of H3PO4, a triprotic weak acid, provides an opportunity to predict, determine, and explain trends in Ka, ΔiH°, and ΔiS°. Trend predictions and analyses provide students an opportunity to use other concepts. For example, students invoke resonance and resonance energy to explain why the H3PO4(aq) neutralization reaction is more exothermic than the HCl(aq) neutralization reaction. Similarly, students must consider solvation to explain changes in entropy. With an equal number of particles on the reactant and the product side, ion−ion attractions and the hydration of ions are needed to explain why ΔiS° values are significantly negative. Students find the experimental procedure to be straightforward. Data analysis (see Supporting Information) is challenging in part because the calculations involve many concepts; some concepts are ones the students have worked with in the past and some are entirely new. To help with data analysis, the instructor goes through a sample calculation prior to the lab. To ensure that students fully comprehend this lab, a post-lab discussion is useful. The post-lab evaluations suggest that students find this lab challenging and yet one in which they learn a lot. It is the multiconcept nature of this lab that makes it an excellent laboratory exercise in general chemistry.

−66.2 ± 2 Run 3 2.06 0.00747 0.0068 ± 0.0007

The density of 2.00 M H3PO4(aq) is 1.10 g/mL.

results obtained by a student participant for H3PO4(aq). Table 2 provides a student’s results for HCl(aq), H2PO4−(aq), and HPO42−(aq). Other students report similar results.

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DISCUSSION The experimental conditions have been set such that the temperature changes in the enthalpy of neutralization reactions are approximately 2−3 °C. With such small temperature changes, heat losses to the surroundings are minimized and stable pre- and post-reaction temperatures are observed. Small temperature changes are acceptable in this case because of the ±0.01 °C sensitivity. Table 2. Summary of a Student’s Results ΔNeutr.H°/

ΔiH°/

ΔiS°/

−TΔiS°/

ΔiG°/

Acid

Ka

(kJ/mol)

(kJ/mol)

(J/K·mol)

(kJ/mol)

(kJ/mol)

HCl(aq) H3PO4(aq) H2PO4−(aq) HPO42−(aq)

NA 6.8 × 10−3 8.1 × 10−8 5.1 × 10−13

−58.2 −66.2 −52.9 −42.5

NA −8.1 5.3 15.7

NA −68.8 −117.8 −182.1

NA 20.3 34.7 53.7

NA 12.2 40.0 69.4

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Laboratory Experiment

ASSOCIATED CONTENT

S Supporting Information *

Notes for the instructor; student handout; spreadsheet with student data. This material is available via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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