Chapter 9 Solutions to Odd Numbered Problems

 

These solutions were provided by Dr. Todd Rayne of Hamilton College

 

1.  How much KCl is in one liter of a 0.26-molar (0.26 M) solution?

 

           

 

3.  The solubility product for CuCl is 10-5.9. What is the solubility of Cu+ at equilibrium with CuCl?

   

           

 

 

 

5.  The solubility product of fluorite, CaF2, is 10 -10.5.

(A)  What is the solubility of Ca2+ at equilibrium with fluorite?

(B)  If CaF2 is dissolved in a solution of 0.009-molar F-, how much will dissolve at equilibrium?

 

A.      

                       

                       

                                               

 

B.  In the new solution, there will be x moles of CaF2 and 0.009 mole of  from the existing solution.

           

           

 

 

7.   Given the following ground-water analysis at 25 oC::

  Ca2+   134 mg/L         HCO3 -  412 mg/L                

  Mg2+  44 mg/L           Cl -       34 mg/L  

  Na+    145 mg/L         pH         8.0

  SO42-  429 mg/L         TDS   1205 mg/L

(A)  Convert all analyses into molal concentrations.

(B)  Compute ionic strength.

(C)  Compute activity coefficient for each ion.

(D)  Find activity of each ion.

(E)  Convert analyses to meq/L.

(F)  Do a cation-anion balance.

(G)  Find the Kiap of anhydrite (CaSO4).

(H)  Compare the Kiap of anhydrite with the Ksp of anhydrite (10-4.5).

(I)   Find the Kiap of calcite (CaCO3).

(J)   Compare the Kiap of calcite with the Ksp of calcite (10-8.35).

   

Ion

Formula Wt

Charge

Ionic.radius

Concentration (mg/l)

Concentrat. (mol/l)

Activity Coeff.

Activity

Concentration (meq/l)

CATIONS

 

 

 

 

 

 

 

 

40.08

2

6

134

3.34E-03

5.63E-01

1.88E-03

6.69

24.31

2

8

44

1.81E-03

5.87E-01

1.06E-03

3.62

Na +

22.99

1

4

145

6.31E-03

8.55E-01

5.39E-03

6.31

 

 

 

Cation total=1.15E-02

 

 

ANIONS

 

 

 

 

 

 

 

 

96.06

2

4

429

4.47E-03

5.35E-01

2.39E-03

8.93

61.01

1

4

412

6.75E-03

8.55E-01

5.78E-03

6.75

35.45

1

3

34

9.59E-04

8.49E-01

8.14E-04

0.96

 

 

 

Anion total=1.22E-02

 

 

Ionic strength= 2.62E-02

 

 

 

 

 

 

 

Charge balance

 

 

 

 

 

 

 

 

cations

1.66E-02

 

 

 

 

 

 

 

anions

1.66E-02

 

 

 

 

 

 

 

c.b. error

acceptable

 

 

 

 

 

 

A.        Convert concentrations in mg/l to mol/l using Eqn. 9-1

 

           

                       

See table for other conversions.

 

B.        Calculate ionic strength using Equation 9-16.

 

           

                       

 

C.        Calculate activity coefficient for each ion using Equation 9-17A

                        e.g.

 

           

                       

 

See table for other activity coefficients

 

D.        Calculate activities using Equation 9-15

 

           

                       

           

See table for other activity calculations.

 

E.        

                                   

                       

                       

See table for other  calculations.

 

F.         Cation - anion balance:

            where

                       

           

 

G.

               

           

 

H.

           

                       

Therefore, the water is 14% saturated with respect to anhydrite.

 

I.

 

J.

            ; Therefore the water is 1140% saturated with respect to calcite.

 

9. What are [H+] and [OH-] for an aqueous solution at pH 9.32?

   

                       [H+] = 10-9.32

 

 

11. What is the pH of a 0.0041-molal solution of H2CO3?

   

Species present: H+, OH-, H2CO3, HCO3-, CO32-

 

Assume:                       1. Most  ions are from

                                    2.  is small (Equation 9-22 A and B)

                                    3.  is small because solution is acidic.

 

           

and using assumptions

from Eqn. 9-22A:

           

and  is small (Assumption 2) and  then .

and assume that  is small relative to [H2CO3] because this is weak acid, so  molal

then:

 

           

13. What is the pH of a 0.0041-molal solution of HCl?

   

            This is a strong acid and will dissociate completely, meaning that  molal

 

           

 

 

 

 

15. The solubility product for barite (BaSO4) is 10-9.97 and the DHoR is 26.6 kJ/mol. R is 8.3143 J/mol-K. What is the solubility product of barite in a hot springs with a temperature of 43°C?

           

Using Eqn. 9-38:         

 

where