Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Question
![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 \( T = 275 \, \text{K} \)?](https://content.bartleby.com/qna-images/question/3c924432-5356-4d2a-9799-f03f3a53c4ab/fb1af54b-0b12-47a7-bd7b-965481d8a411/uasxhvj_processed.png)
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 \( T = 275 \, \text{K} \)?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Similar questions
- Calculate The change in the Gibbs free energy for each set of delta H reaction Delta S reaction and tea assume the reactants and products are in their standard states. DeltaHrxn= +123 kJ, DeltaSrxn= -244 J/K; T=290 Karrow_forwardKm.201.arrow_forward(a) Choose all of the statements from below which correctly describe issues pertaining to the relationship between the emf of a reaction and its Gibbs free energy change. ____The Gibbs free energy change and emf values of a reaction have opposite algebraic signs (+ vs. -).____A Gibbs free energy change involves moles of substances whereas an emf involves coulombs of electrons.____A coulomb of particles is more particles than a mole of particles.____Faraday's constant is not used to interconvert a Gibbs free energy change and a reaction emf.____A Gibbs free energy change involves coulombs of substances whereas an emf involves moles of electrons.Calculate the standard Gibbs free energy changes at 25 oC for each of the reactions shown below using the Eo values given. Select whether each of these reactions is nonspontaneous, at equilibrium, or spontaneous under standard conditions. (a) 1 Al3+(aq) + 3 Ag(s) 1 Al(s) + 3 Ag+(aq) Eo = -2.459 V Go =________ kJ/mol ____nonspontaneous…arrow_forward
- For a certain chemical reaction, the standard Gibbs free energy of reaction at 15.0 °C is 147. kJ . Calculate the equilibrium constant K for this reaction.Round your answer to 2 significant digits.arrow_forwardFor a certain chemical reaction, the standard Gibbs free energy of reaction at 30.0°C is 73.3 kJ. Calculate the equilibrium constant K for this reaction. Round your answer to 2 significant digits.arrow_forwardUse the following information to calculate the standard free energy change (AG°) and equilibrium constant (K) for the following system: CaCO3(s) = CaO(s) + CO2(g) T= 900.0 °C AH;° values (kJ/mol): CaO(s) = -634.9, CO2(g) = -393.51, CaCO3(s) =–1220.0 %3D S° values (J/mol K): CaO(s) = 110.0, CO2(g) = 213.8, CACO3(s) = 38.1 %3D %3D %3Darrow_forward
- For a certain chemical reaction, the standard Gibbs free energy of reaction at 20.0 °C is 90.2 kJ. Calculate the equilibrium constant K for this reaction. Round your answer to 2 significant digits. K = || x10arrow_forward[Review Topics] [References] Use the References to access important values if needed for this question. Consider the following system at equilibrium where AH° = -111 kJ/mol, and K. = 0.159 , at 723 K. N2 (g) + 3 H, (g)=2 NH3 (g) When 0.21 moles of NH, (g) are added to the equilibrium system at constant temperature: The value of K The value of Qe K. The reaction must O run in the forward direction to restablish cquilibrium. O run in the reverse direction to restablish coquilibrium. O remain the same. It is already at cquilibrium. The concentration of H, will Submit Answer Retry Entire Group 1 more group attempt remainingarrow_forwardCalculate the standard change in Gibbs free energy for the reaction at 25 °C. Standard Gibbs free energy of formation values can be found in this table. 3 NO₂(g) + H₂O(1) AGixn || - 2 HNO3 (1) + NO(g) kJ/molarrow_forward
- Calculate The Equilibrium Constant K of hydrosulfuric acid (H2S(aq)) Standard Gibbs Free energy for H2S(aq) is -27.7Then, Calculate the pKa1 and pKa2 of hydrosulfuric acidarrow_forward11. What is the ΔHº-value for the dissolution of NaOH (s) to yield 1.00... m NaOH (aq), given: Na (s) + 1/2 O2 (g) + 1/2 H2 (g) → NaOH (s) ΔHfº = -425.9 kJ/mol Na (s) + 1/2 O2 (g) + 1/2 H2 (g) → NaOH (aq, 1 m) ΔHfº = -469.2 kJ/mol Multiple Choice -895.1 kJ/mol -43.3 kJ/mol +1.102 kJ/mol +43.3 kJ/mol +895.1 kJ/molarrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage Learning
ChemistryChemistryISBN:9781259911156Author:Raymond Chang Dr., Jason Overby ProfessorPublisher:McGraw-Hill Education
Principles of Instrumental AnalysisChemistryISBN:9781305577213Author:Douglas A. Skoog, F. James Holler, Stanley R. CrouchPublisher:Cengage Learning 
Organic ChemistryChemistryISBN:9780078021558Author:Janice Gorzynski Smith Dr.Publisher:McGraw-Hill Education
Chemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage Learning
Elementary Principles of Chemical Processes, Bind...ChemistryISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEY
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning
Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY