Kw(293 K) = 0.67 × 10-14 M² Kw(298 K) = 1.00 × 10-14 M² Kw(303 K) = 1.45 × 10-14 M² Assuming that the value of AH° and AS° are constant over this narrow temperature range, determine their values (in kJ/mol and J/mol-K, respectively for the ionization equilibrium at 298 K based on this information. (Hint: You should use both the relationship between AG° and K, and the relationship between the Gibbs energy, enthalpy, and entropy in this problem. Setting up your analysis as a least-squares linear fit provides the best result.) Based on the results from part (a), what would you expect the autoionization equilibrium constant to be near the freezing point of water, at T = 275 K?

Principles of Modern Chemistry
8th Edition
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Chapter16: Solubility And Precipitation Equilibria
Section: Chapter Questions
Problem 70AP
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An equilibrium constant of special importance in much aqueous chemistry is that of the
autoionization of water:
2 H₂O (/) H3O+ (aq) + OH¯ (aq)
Kw
The value of this equilibrium constant at three temperatures near standard temperature is
Kw(293 K) = 0.67 × 10-¹4 M²
Kw(298 K) = 1.00 × 10-¹4 M²
Kw(303 K) = 1.45 × 10-¹4 M²
(a) Assuming that the value of AH° and AS° are constant over this narrow temperature
range, determine their values (in kJ/mol and J/mol-K, respectively for the ionization
equilibrium at 298 K based on this information. (Hint: You should use both the
relationship between AG° and K, and the relationship between the Gibbs energy,
enthalpy, and entropy in this problem. Setting up your analysis as a least-squares linear
fit provides the best result.)
(b) Based on the results from part (a), what would you expect the autoionization
equilibrium constant to be near the freezing point of water, at T = 275 K?
Transcribed Image Text:An equilibrium constant of special importance in much aqueous chemistry is that of the autoionization of water: 2 H₂O (/) H3O+ (aq) + OH¯ (aq) Kw The value of this equilibrium constant at three temperatures near standard temperature is Kw(293 K) = 0.67 × 10-¹4 M² Kw(298 K) = 1.00 × 10-¹4 M² Kw(303 K) = 1.45 × 10-¹4 M² (a) Assuming that the value of AH° and AS° are constant over this narrow temperature range, determine their values (in kJ/mol and J/mol-K, respectively for the ionization equilibrium at 298 K based on this information. (Hint: You should use both the relationship between AG° and K, and the relationship between the Gibbs energy, enthalpy, and entropy in this problem. Setting up your analysis as a least-squares linear fit provides the best result.) (b) Based on the results from part (a), what would you expect the autoionization equilibrium constant to be near the freezing point of water, at T = 275 K?
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