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?
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?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![An equilibrium constant of special importance in much aqueous chemistry is that of the autoionization of water:
\[ 2 \, \text{H}_2\text{O (l)} \rightleftharpoons \text{H}_3\text{O}^+ \, \text{(aq)} + \text{OH}^- \, \text{(aq)} \quad K_w \]
The value of this equilibrium constant at three temperatures near standard temperature is:
\[ K_w(293 \, \text{K}) = 0.67 \times 10^{-14} \, \text{M}^2 \]
\[ K_w(298 \, \text{K}) = 1.00 \times 10^{-14} \, \text{M}^2 \]
\[ K_w(303 \, \text{K}) = 1.45 \times 10^{-14} \, \text{M}^2 \]
(a) Assuming that the value of \( \Delta H^\circ \) and \( \Delta S^\circ \) 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 \( \Delta G^\circ \) 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 \( T = 275 \, \text{K} \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c924432-5356-4d2a-9799-f03f3a53c4ab%2Ffb1af54b-0b12-47a7-bd7b-965481d8a411%2Fuasxhvj_processed.png&w=3840&q=75)
Transcribed Image Text:An equilibrium constant of special importance in much aqueous chemistry is that of the autoionization of water:
\[ 2 \, \text{H}_2\text{O (l)} \rightleftharpoons \text{H}_3\text{O}^+ \, \text{(aq)} + \text{OH}^- \, \text{(aq)} \quad K_w \]
The value of this equilibrium constant at three temperatures near standard temperature is:
\[ K_w(293 \, \text{K}) = 0.67 \times 10^{-14} \, \text{M}^2 \]
\[ K_w(298 \, \text{K}) = 1.00 \times 10^{-14} \, \text{M}^2 \]
\[ K_w(303 \, \text{K}) = 1.45 \times 10^{-14} \, \text{M}^2 \]
(a) Assuming that the value of \( \Delta H^\circ \) and \( \Delta S^\circ \) 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 \( \Delta G^\circ \) 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 \( T = 275 \, \text{K} \)?
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