Laboratory Experiment pubs.acs.org/jchemeduc
Weak Acid Ionization Constants and the Determination of Weak Acid−Weak Base Reaction Equilibrium Constants in the General Chemistry Laboratory Frazier Nyasulu,* Lauren McMills, and Rebecca Barlag Department of Chemistry and Biochemistry, Ohio University, Athens, Ohio 45701, United States S Supporting Information *
ABSTRACT: A laboratory to determine the equilibrium constants of weak acid−weak base reactions is described. The equilibrium constants of component reactions when multiplied together equal the numerical value of the equilibrium constant of the summative reaction. The component reactions are weak acid ionization reactions, weak base hydrolysis reactions, and the auto-ionization of water reaction. The summative equations are weak acid−weak base reactions. The acid ionization constants (Ka) of HC2H3O2, H3PO4, H2PO4−, HPO42−, and NH4+ are determined from measurements of the pH in buffer solutions with known weak acid and known weak base concentrations, and base hydrolysis constants (Kb) are determined using Ka × Kb = Kw. KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Acids/Bases, Aqueous Solution Chemistry Equilibrium, pH
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majority of general chemistry programs include a laboratory in which Hess’s law is explored.1,2 According to Hess’s law, the sum of the enthalpy of component reactions is equal to the enthalpy of the summative reaction. A general chemistry laboratory that is similar is described, but instead of using enthalpy, it is based on equilibrium constants. If component reactions add to a summative equation, the equilibrium constants of component reactions multiplied together equal the numerical value of the equilibrium constant of the summative reaction. The component reactions are acid ionization reactions and base hydrolysis reactions and the summative equations are weak acid−weak base reactions. This work builds on the publication by Thompson in this Journal.3 Students derive each of the overall summative weak acid− weak base reactions by combining component reactions consisting of weak acid ionization reactions, weak base hydrolysis reactions, and the autoionization of water reaction. The equilibrium constants of the component reactions are weak acid ionization constants (Ka), weak base hydrolysis reaction constants (Kb), and the water autoionization constant (Kw). The values of Ka and Kb are determined from pH measurements in buffer solutions with known concentrations of weak acid and corresponding conjugate base.4−7 The buffer solutions are HC 2 H 3 O 2 (aq)/C 2 H 3 O 2 − (aq), NH 4 + (aq)/NH 3 (aq), H3PO4 (aq)/H 2PO4 −(aq), H2PO4 −(aq)/HPO 42−(aq), and HPO42−(aq)/PO43−(aq). The equilibrium constants of the component reactions (Ka, Kb, and Kw) are then multiplied to obtain the equilibrium constant of the summative equation (Kc); Kw does not appear in the Kc expressions. The weak acid−weak base summative reactions whose Kc values are determined are given in Table 1. In addition to the determination of Kc values, the students also determine which of the reactions achieve ≥99% reaction completion. © XXXX American Chemical Society and Division of Chemical Education, Inc.
THEORY
Weak Acid Ionization Constants (Ka), Weak Base Hydrolysis Constants (Kb)
If the pH of a known buffer solution is measured, pKa can be calculated according to the Henderson−Hasselbalch equation: pH = pK a + log
n(A−) [A−] = pK a + log [HA] n(HA)
(1)
where n(X) is the amount of X. If pKa (or Ka) is known, pKb (or Kb) can be calculated from Kw expressions: pK a(HA) + pKb(A−) = pK w
K a(HA) × Kb(A−) = K w (2)
For H3PO4, the acid ionization reactions and acid ionization constants are defined in the regular way. Unlike acids, the numbering in base hydrolysis reactions can vary. Herein the hydrolysis reactions and base hydrolysis constants are defined as PO4 3 −(aq) + H 2O(l) ⇆ HPO4 2 −(aq) + OH−(aq) Kb1 =
[OH−][HPO4 2 −] [PO4 3 −]
(3)
HPO4 2 −(aq) + H 2O(l) ⇆ H 2PO4 −(aq) + OH−(aq) Kb2 =
[OH−][H 2PO4 −] [HPO4 2 −] (4)
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dx.doi.org/10.1021/ed300403v | J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Laboratory Experiment
Table 1. Typical Kc, Qc, and Reaction Completion Outcome Qc
≥99% Reaction
HC2H3O2 (aq) + NH3(aq) → NH4 +(aq) + C2H3O2−(aq)
K a(HC2H3O2 ) = 3.8 × 104 K a(NH4 +)
9.8 × 103
Yes
HPO4 2 −(aq) + NH3(aq) → NH4 +(aq) + PO4 3 −(aq)
K a3(H3PO4 ) = 1.1 × 10−3 K a(NH4 +)
9.8 × 103
No
H 2PO4 2 −(aq) + NH3(aq) → NH4 +(aq) + HPO4 2 −(aq)
K a2(H3PO4 ) = 1.8 × 102 K a(NH4 +)
9.8 × 103
No
9.7 × 108
No
Kc
Reaction
H3PO4 (aq) + 3NH3(aq) → 3NH4 +(aq) + PO4 3 −(aq)
K a1(HC2H3O2 )×K a2(HC2H3O2 )×K a3(H3PO4 ) K a(NH4 +)3
= 3.1 × 106
2H3PO4 (aq) + PO4 3 −(aq) → 3H 2PO4−(aq)
⎣⎡K a1(H3PO4 )⎦⎤2 = 1.1 × 1015 K a2(H3PO4 ) × K a3(H3PO4 )
9.6 × 107
Yes
H3PO4 (aq) + HPO4 2 −(aq) → 2H 2PO4−(aq)
K a1(H3PO4 ) = 8.4 × 104 K a2(H3PO4 )
9.8 × 103
Yes
H 2PO4 −(aq) + H 2O(l) ⇆ H3PO4 (aq) + OH−(aq) Kb3 =
[OH−][H3PO4 ] [H 2PO4 −]
approach leads to polynomial equations that are difficult to solve. One way to avoid difficult polynomial equations is to assume 99% reaction completion, calculate the reaction quotient (Qc), and compare Qc to Kc. To make assessment manageable, the initial reactant molarities are assumed to be in the same ratio as their stoichiometric coefficients in the balanced chemical equation. As an example, consider the following reaction in which the starting H3PO4(aq) and NH3(aq) are assumed to be 0.10 and 0.20 M, respectively.
(5)
With these, the Kw expressions are K a1(H3PO4 ) × Kb3(PO4 3 −) = K w
(6)
K a2(H3PO4 ) × Kb2(PO4 3 −) = K w
(7)
K a3(H3PO4 ) × Kb1(PO4 3 −) = K w
(8)
H3PO4 (aq) + 2NH3(aq) → 2NH4 +(aq) + HPO4 2 −(aq)
Allowing 99% of the starting reactants to react, the concentrations after reaction are 0.001 M H3PO4(aq), 0.002 M NH3(aq), 0.198 M NH4+(aq), and 0.099 M HPO42−(aq). Qc is calculated to be
Derivation of the Weak Acid−Weak Base Equilibrium Constant
Because Ka values are determined, the component reactions are written in terms of Ka and or Kw. Consider the following weak acid−weak base reaction as an example:
Qc =
H3PO4 (aq) + 2NH3(aq) → 2NH4 +(aq) + HPO4 2 −(aq)
[NH4 +]2 [HPO4 2 −] 2
[NH3] [H3PO4 ]
=
0.1982 × 0.099 0.0022 × 0.001
= 9.70 × 105
(9)
If Qc < Kc, the reaction would need to react more than 99% in order to increase the numerator and decrease the denominator and thereby increase Qc toward Kc. Therefore, if Qc < Kc, the reaction is ≥99% complete, and if Qc > Kc, the reaction does not achieve 99% completion.
Equation 9 can be written as a sum of four acid−base reactions:
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EXPERIMENTAL DETAILS
Materials and Equipment
Pasco Scientific datalogger, Pasco Scientific pH sensor, stirrer, stir bars, stir bar retrievers, autopipettors, 1.0 M H3PO4(aq), 1.0 M NaH2PO4(aq), 1.0 M K2HPO4(aq), 1.0 M Na3PO4(aq), 1.0 M NH4Cl(aq), 1.0 M NH3(aq), 1.0 M HC2H3O2(aq), 1.0 M Na HC2H3O2(aq), pH 4.00 buffer, and pH 10.00 buffer. Procedure
Kc for the overall equation (eq 9 or eq 14) is equal to the product of the equilibrium constants of component reactions: Kc =
Students work in pairs. The time required to make the experimental measurements is about an hour and the lab period is 3 h. The pH sensor is calibrated using pH 4.00 and pH 10.00 buffers. A stir bar and 3.00 mL of the weak acid are added to a 6-in. test tube. A pH sensor is placed in the same test tube, and using a wash bottle, deionized water is added such that the sensitive part of the pH sensor is submerged. Small aliquots, 1.00 mL, of the conjugate base are added, the solution is stirred, and the pH is measured after each addition. A total of three
K a1(H3PO4 ) × K a2(H3PO4 ) K a(NH4 +)2
(15)
Assessment of Which Reactions Achieve ≥99% Completion
With Kc determined and given known initial reagent concentrations, students could calculate the equilibrium concentration of reactants and products. Unfortunately, this B
dx.doi.org/10.1021/ed300403v | J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
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1.00 mL aliquots of conjugate base are added so that an average Ka can be calculated.
Laboratory Experiment
REFERENCES
(1) Peck, L.; Irgolic, K. J. Measurement and Synthesis in the Chemistry Laboratory, 2nd ed.; Prentice Hall: Upper Saddle River, NJ, 1992; pp 311−324. (2) Szafran, Z.; Pike, R. M.; Foster, J. C. Microscale General Chemistry Laboratory with Selected Macroscale Experiments; John Wiley: New York, NY, 1993; pp 303− 316. (3) Thompson, R. J. J. Chem. Educ. 1990, 67, 220−221. (4) Nyasulu, F.; Moehring, M.; Arthasery, P.; Barlag, R. J. Chem. Educ. 2011, 88, 640−642. (5) Sanger, M. J.; Danner, M. J. Chem. Educ. 2010, 87, 1213−1216. (6) Neidig, H. A.; Yingling, R. T. J. Chem. Educ. 1965, 45, 485. (7) Clement, G. E.; Hartz, T. P. J. Chem. Educ. 1971, 48, 395−397.
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HAZARDS Na3PO4(aq) is caustic and may require handling with gloves. All other reagents are weak acids but should also be handled with care. Any contact with skin should be rinsed with plenty of water.
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RESULTS After measuring the pH, pKa is calculated according to eq 1. Ka values reported by a student are HC2H3O2 (aq): 1.8 ( ±0.2) × 10−5
NH4 +(aq): 4.5 ( ±0.2) × 10−10 H3PO4 (aq): K a1 = 6.8 ( ±0.2) × 10−3 K a2 = 8.1 (± 0.2) × 10−8 K a3 = 5.1 (± 0.3) × 10−13
The majority of the laboratory period (3 h) is spent deriving the Kc expressions. Kc expressions and Qc values for the six reactions are shown in Table 1.
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CONCLUSION With small aliquots of weak acid and weak base solutions added to a test tube and the pH measured, the procedure is not only easily and quickly implemented, but it also conserves materials. In summary, (i) the equipment needs are minimal; a pH meter. (ii) This lab adds to students’ understanding of acid−base reactions. (iii) Ka values are determined. (iv) The derivations are challenging, but manageable and provide significant practice at deriving component reactions that add up to a specific summative reaction. The laboratory setting provides an opportunity for students to work with each other to solve problems that would otherwise be too difficult. (v) The determination of which reactions go to completion provides an opportunity for students to further understand quantitative aspects of equilibrium constants. A Kc of 106 may or may not be enough for quantitative reaction; it all depends on the reaction’s stoichiometry and reagent concentrations ratio. (vi) These calculations are performed six times; this repetition increases the likelihood that students understand the material. (vii) The instructor can decrease the length and complexity of this lab by omitting some reactions.
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ASSOCIATED CONTENT
S Supporting Information *
Notes for the instructor and student handout. 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. C
dx.doi.org/10.1021/ed300403v | J. Chem. Educ. XXXX, XXX, XXX−XXX
