Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
8th Edition
ISBN: 9781305079373
Author: William L. Masterton, Cecile N. Hurley
Publisher: Cengage Learning
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Chapter 16, Problem 81QAP
Interpretation Introduction

Interpretation:

The first and second ionization constants for sulfuric acid, H2 SO4 need to be calculated.

Concept introduction:

  1. Ionization constant or dissociation constant is a value which is used to measure the strength of acids (Ka ) and bases (Kb ). These are essentially equilibrium constants which are expressed as the ratio between the dissociated and undissociated forms.
  2. The ionization constant is related to the standard Gibbs free energy ΔG° by the following equation:
  3. ΔG0 = -RTlnKeq -----(1)where Keq = Ka or Kb

  4. The standard Gibbs free energy ΔG0 for a given chemical reaction can be expressed as a function of temperature, T via the Gibbs-Helmholtz equation:
  5. ΔG0 = ΔH0 - TΔS0 -------(2)

    where, ΔH0 is the standard enthalpy change, and ΔS0 is the standard entropy change

  6. The standard enthalpy change for a reaction ΔH0 is given in terms of the difference in the standard enthalpy of formation of the products and that of reactants.
  7. ΔH0 = npΔHf0(products) - nrΔHf0(reactants)  ------(3)

    Where np and nr are the number of moles of the products and reactants

  8. The standard entropy change for a reaction ΔS0 is given in terms of the difference in the standard entropy of formation of the products and that of reactants.
  9. ΔS0 = npSf0(products) - nrSf0(reactants) -------(4)

    Where np and nr are the number of moles of the products and reactants.

Expert Solution & Answer
Check Mark

Answer to Problem 81QAP

Ka1 = 1.0 ×103Ka2 = 1.0×102

Explanation of Solution

Given:

ΔHf0(H2SO4) = -902.9 kJS0(H2SO4) = 17.14 J/K

The dissociation of H2 SO4 can be expressed as

H2SO4(aq)2H+(aq) + SO42-(aq)

This is a two-step process each associated with a Ka value as shown below:

H2SO4(aq)H+(aq) + HSO4-(aq)         Ka1 -------(1)HSO4-(aq)   H+(aq) + SO42-(aq)         Ka2 --------(2)

The value of Ka1 and Ka2 can be calculated by deducing the ΔG° value for reactions (1) and (2) and substituting the appropriate values in equation (1):

Step 1: Calculate ΔG° for the overall dissociation of H2 SO4.

The dissociation of H2 SO4 is represented as H2SO4(aq)2H+(aq) + SO42-(aq)

From equation (3), ΔH° for the above reaction is

ΔH0 = [2ΔHf0(H+(aq)) + 1ΔHf0(SO42-(aq))] - [1ΔHf0(H2SO4(aq)) ]Based on the ΔHf0 values:ΔH0 = [2 mole ×(0 kJ/mol) + 1 mole ×(-907.51 kJ/mol)]-[1 mole ×(902.9 kJ/mol)]         = 0 - 907.51+ 902.9  = -4.61 kJ         

From equation (4), S° for the above reaction is

ΔS0 = [2Sf0(H+(aq)) + 1Sf0(SO42-(aq))] - [1Sf0(H2SO4(aq)) ]Based on the ΔHf0 values:ΔS0 = [2 mole ×(0 J/mol-K) + 1 mole ×(20.1 J/mol-K)]-[1 mole ×(17.14 J/mol-K)]         = 0 + 20.1 - 17.14  = 2.96 J/mol-K         

At T = 298 K,

ΔG0 = ΔH0 - TΔS0=4.61(298)(0.00296)=5.49 kJ

Step 2: Calculate ΔG° for the reaction (1) depicted in the two step process.

The reaction (1) is represented as

H2SO4(aq)H+(aq) + HSO4-(aq)

From equation (3), ΔH° for the above reaction is

ΔH0 = [2ΔHf0(H+(aq)) + 1ΔHf0(HSO4-(aq))] - [1ΔHf0(H2SO4(aq)) ]Based on the ΔHf0 values,ΔH0 = [2 mole ×(0 kJ/mol) + 1 mole ×(-885.75 kJ/mol)]-[1 mole ×(902.9 kJ/mol)]         = 0 - 885.75 + 902.9  = 17.15 kJ         

From equation (4), S° for the above reaction is

ΔS0 = [2Sf0(H+(aq)) + 1Sf0(HSO4-(aq))] - [1Sf0(H2SO4(aq)) ]Based on the Sf0 values,ΔS0 = [2 mole ×(0 J/mol-K) + 1 mole ×(131.8 J/mol-K)]-[1 mole ×(17.14 J/mol-K)]         = 0 + 131.8 - 17.14  = 114.66 J/mol-K         

At T = 298 K,

ΔG0 = ΔH0 - TΔS0=17.15(298)(0.1147)=0.12 kJTherefore, ΔG10= -17.02 kJ

Step 3: Calculate ΔG° for the reaction (2) depicted in the two step process.

The overall reaction is the sum of reactions (1) and (2). Therefore,

ΔG = ΔG10 + ΔG20ΔG20=ΔGΔG10ΔG20=(5.49)(17.02)=+11.53 kJ

Step 4: Calculate Ka1 and Ka2.

ΔG10 = -RTlnKa1Ka1 = e-ΔG10RTΔG10 =-11.53 kJ; R = 0.008314 kJ/K-mol; T = 298 K

Ka1 = e11.530.008314×298=9621×103ΔG20 = -RTlnKa2Ka2 = e-ΔG20RTΔG20 =11.53 kJ; R = 0.008314 kJ/K-mol; T = 298 KKa2 = e11.530.008314×298=0.009531.0×102

Conclusion

The ionization constants for H2SO4 are: Ka1 = 1.0 ×103 and Ka2 = 1.0×102.

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Chapter 16 Solutions

Chemistry: Principles and Reactions

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