Chapter 11

Solving Equilibrium Problems for Complex Systems

For example, if our task is to compute the solubility of barium sulfate in an acidic solution, there are three equilibria:

We must calculate the concentrations of all the species in the solution. In this example, there are five species:

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11A Solving Multiple-Equilibrium Problems

• 다중평형계에 존재하는 화학종들의 수만큼 독립적인 방정식이 필요함

11A-1 Mass-Balance Equations

let us explore the details of what happens when a weak acid HA is dissolved in water with a molar analytical concentration of cHA.

cHA = [HA] + [A-]

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11A-2 Charge-Balance Equations

The charge balance is an algebraic statement of electroneutrality of the solution. That is the sum of the positive charges in an electrolyte solution equals the sum of the negative charges in solution.

Solution must have zero total charge.

no. mol/L positive charge = no. mol/L negative charge

Σ[positive charges] = Σ[negative charges]

The general form of the charge balance for any solution:

n1[C1] + n2[C2] + … = m1[A1] + m2[A2] + ... where ni = charge of the ith cation [Ci] = concentration of the ith cation mi = charge of the ith anion [Ai] = concentration of the ith anion

Ex) 0.1 M NaCl의 charge balance equation?

Ex) 0.1 M MgCl2의 charge balance equation?

Example 11-3. 0.010 M NH3 solution saturated with AgBr

Pertinent equilibria:

AgBr(solid) ↔ Ag+ (aq)

+ Br– (aq)

Ag+ (aq)

+ 2NH3 (aq) → Ag(NH3)+

(aq)

Ag(NH3)+ + NH3 ↔ Ag(NH3)2

+

NH3 + H2O ↔ NH4+ + OH–

2H2O ↔ H3O+ + OH–

Mass balance equations:

[Ag+] + [Ag(NH3)+] + [Ag(NH3)2

+] = [Br–]

cNH3 = [NH3] + [NH4+] + [Ag(NH3)

+] + [Ag(NH3)2+] = 0.010

[OH–] = [NH4+] + [H3O+]

Charge balance :

[Ag+] + [Ag(NH3)+] + [Ag(NH3)2

+] + [NH4+] + [H3O+] = [OH–] + [Br–]

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11A-3 Steps for Solving Problems Involving Several Equilibria

1. Write a set of balanced chemical equations for all pertinent equilibria.

2. Set up equation for unknown quantity : Define the unknown.

3. Write all equilibrium-constant expressions.

4. Write mass balance expressions for the system.

5. If possible, write the charge balance expression for the system.

6. Count the number of independent equations and unknowns.

7. Make suitable approximations to reduce the number of unknowns.

8. Solve the simultaneous equations.

9. Check the validity of the approximations.

11A-4 Using Approximations to Solve Equilibrium Calculations

11A-5 Use of Computer Programs to Solve Multiple-Equilibrium Calculations

11B Calculating Solubilities by the Systematic Method

11B-1 The Solubility of Metal Hydroxides

Systematic method를 이용하여 여러 가지 조건에서 침전들의 solubility를 구함.

Remind processes !!!

11B-2 The Effect of pH on Solubility

Solubility Calculations When the pH Is Constant