CEE 680

4 October 2001

 

FIRST EXAM

 

 

Closed book, one page of notes allowed.

 

Answer all questions.  Please state any additional assumptions you made, and show all work.  You are welcome to use a graphical method of solution if it is appropriate.

 

 

   Miscellaneous Information:

                    R =  1.987 cal/mole°K = 8.314 J/mole°K

                          Absolute zero = -273.15°C

                    1 joule = 0.239 calories

                    1015 calories = 1 Big Mac

 

 

1.                  (50%) What is the pH of a 10-2.65 M solution of Sodium fluoride (NaF)?  Calculate this for each of the three conditions below.

 

                           a. 25°C, I = 0

                           b. 100°C, I = 0

                           c. 25°C, I = 0.25

 

Preferred Approach

·         recognize that this is a simple base problem

·         then adopt an appropriate set of assumptions, and solve for [H+]

·         finally correct pKa (and pKw) for temperature, ionic strength, and repeat

·         check assumptions

 

a.  25°C, I = 0

Assume a weak base: [F-] >> [HF]

 

 

if the pKa for HF/F (at 25° C and I=0) is 3.2, then the pKb is 14-3.2 or 10.8

 

 

 

pH = 7.33

 

 

Check Assumptions:

[F-] >> [HF] or:

 

 

,     YES!!!

 

 

b.  100°C, I = 0

 

determine enthalpy change for the reaction:

                           HF = H+ + F-

 

then re-estimate Ka

 

 

K100 = 2.34 x 10-4

 

 

and now:

As before, assume a weak base: [F-] >> [HF]

 

 

if the pKa for HF/F (at 100° C and I=0) is 3.63, then the pKb is 14-3.63 or 10.37

 

 

 

pH = 7.51

 

 

Check Assumptions:

[F-] >> [HF] or:

 

 

,     YES!!!

 

Now, strictly speaking, you would also need to adjust Kw for the higher temperature as well.

 

 

 

c.  25°C, I = 0.25

 

determine activity coefficients for the species in the reaction:

                           HF = H+ + F-

And for

                           H2O = H+ + OH-

For this level, use the simple Davies equation for the charged species, and assume no change in the activity of theuncharged species:

 

 

so:

 

 

 

 

then re-estimate Ka and Kw under this condition, i.e., the conditional K’s

 

 

and:

 

 

and now:

As before, assume a weak base: [F-] >> [HF]

 

 

if the pKa for HF/F (at 25° C and I=0.25) is 2.92, then the pKb is 13.72-2.92 or 10.80

 

 

 

now we must recognize that pH is related to proton activity not concentration

 

pH = 7.23

 

 

Check Assumptions:

[F-] >> [HF] or:

 

 

,     YES!!!

 

 

 

2.                  (40%) What is the complete composition of a 1-liter volume of water to which you have added 10-3 M of sodium carbonate (Na2CO3) and 10-2 M of acetic acid?  Approximate values (± 0.2 log units) will suffice.

 

 

 

Approach

·         prepare a logC vs pH diagram for carbonate system (CT=0.001 M) and the acetic acid system (CT = 0.01M) superimposed over it.

·         write the PBE and find a solution

·         read off concentrations from the graph

 

 

the PBE is:

 

2[H2CO3] + [HCO3-] + [H+] = [OH-] + [Ac-]

 

from the graph below, we can conclude that the solution lies at:

2 [H2CO3] = [Ac-]

 

 

pH =4.15

[H+] = 7.0 x 10-5

log [H2CO3] = -3.0

[H2CO3] = 1.0 x 10-3

log [HCO3-] = -5.2

[HCO3-] = 6.3 x 10-6

log [CO3-2] = -11.38

[CO3-2] = 4.2 x 10-12

log [HAc] = -2.10

[HAc] = 8 x 10-3

log [Ac-] = -2.70

[Ac-] = 2 x 10-3

log [OH-] = -9.85

[OH-] = 1.4 x 10-10

 

 

 

 

 

 

 

 

 

 

 

 

 

3.                  (10%) True/False.  Mark each one of the following statements with either a "T" or an "F".

 

a. F____ An increase in ionic strength tends to shift equilibria toward the side with lesser charged species.

 

b. T____ The strong acid assumption is best when pHs are high..

 

c. T____ Hydrogen ions do not usually exist in a free state in water.

 

d. T____ Strong acids will almost completely donate their exchangeable hydrogen ions to the surrounding solvent molecules

 

e. T or F Reactions involving 3 or more molecules cannot be elementary

 

f.  F____ Sodium Acetate is an amphoteric substance.

 

g. T____ Strong acids always result in lower pHs when added to water than weak acids, when both are added at the same concentration.

 

h. F____ Positive DH values indicate that the reaction is exothermic

 

i.  F____ The standard assumption used for calculating the pH of an acidic solution is that the [H+] is negligible.

 

j.  T____ For a monoprotic acid, the value of ao plus a1 must always equal unity.

 

 

 

Selected Acidity Constants  (Aqueous Solution, 25°C, I = 0)

   NAME

   FORMULA

 pKa

Perchloric acid

HClO4 = H+ + ClO4-

-7         STRONG

Hydrochloric acid

HCl = H+ + Cl-

-3

Sulfuric acid

H2SO4= H+ + HSO4-

-3  (&2)    ACIDS

Nitric acid

HNO3 = H+ + NO3-

-0               

Hydronium ion

H3O+ = H+ + H2O

 0               

Trichloroacetic acid

CCl3COOH = H+  + CCl3COO-

 0.70

Iodic acid

HIO3 = H+ + IO3-

 0.8

Bisulfate ion

HSO4- = H+ + SO4-2

 2

Phosphoric acid

H3PO4 = H+ + H2PO4-

 2.15 (&7.2,12.3)

o-Phthalic acid

C6H4(COOH)2 = H+  + C6H4(COOH)COO-

 2.89  (&5.51)

Citric acid

C3H5O(COOH)3= H+  + C3H5O(COOH)2COO-

 3.14 (&4.77,6.4)

Hydrofluoric acid

HF = H+  + F-

 3.2

Aspartic acid

C2H6N(COOH)2= H+  + C2H6N(COOH)COO-

 3.86  (&9.82)

m-Hydroxybenzoic acid

C6H4(OH)COOH = H+  + C6H4(OH)COO-

 4.06  (&9.92)

p-Hydroxybenzoic acid

C6H4(OH)COOH = H+  + C6H4(OH)COO-

 4.48  (&9.32)

Nitrous acid

HNO2 = H+  + NO2-

 4.5

Acetic acid

CH3COOH = H+  + CH3COO-

 4.75

Propionic acid

C2H5COOH = H+  + C2H5COO-

 4.87

Carbonic acid

H2CO3 = H+  + HCO3-

 6.35 (&10.33)

Hydrogen sulfide

H2S = H+  + HS-

 7.02 (&13.9)

Dihydrogen phosphate

H2PO4- = H+  + HPO4-2

 7.2

Hypochlorous acid

HOCl = H+  + OCl-

 7.5

Boric acid

B(OH)3 + H2O = H+  + B(OH)4-

 9.2 (&12.7,13.8)

Ammonium ion

NH4+ = H+  + NH3

 9.24

Hydrocyanic acid

HCN = H+  + CN-

 9.3

p-Hydroxybenzoic acid

C6H4(OH)COO-  = H+  + C6H4(O)COO-2

 9.32

Phenol

C6H5OH = H+  + C6H5O-

 9.9

m-Hydroxybenzoic acid

C6H4(OH)COO-  = H+  + C6H4(O)COO-2

 9.92

Bicarbonate ion

HCO3- = H+  + CO3-2

10.33

Monohydrogen phosphate

HPO4-2  = H+  + PO4-3

12.3

Bisulfide ion

HS-  = H+  + S-2

13.9          

Water

H2O = H+  + OH-

14.00         

Ammonia

NH3 = H+  + NH2-

23

Methane

CH4 = H+ + CH3-

34

 

Species

kcal/mole

kcal/mole

Ca+2(aq)

‑129.77

‑132.18

CaC03(s), calcite

‑288.45

‑269.78

CaO (s)

‑151.9

‑144.4

C(s), graphite

0

0

CO2(g)

‑94.05

‑94.26

CO2(aq)

‑98.69

‑92.31

CH4 (g)

‑17.889

‑12.140

H2CO3 (aq)

‑167.0

‑149.00

HCO3- (aq)

‑165.18

‑140.31

CO3-2 (aq)

‑161.63

‑126.22

CH3COO-, acetate

‑116.84

‑89.0

H+ (aq)

0

0

H2 (g)

0

0

HF (aq)

-77.23

-71.63

F- (aq)

-80.15

-67.28

Fe+2 (aq)

‑21.0

‑20.30

Fe+3 (aq)

‑11.4

‑2.52

Fe(OH)3 (s)

‑197.0

‑166.0

NO3- (aq)

‑49.372

‑26.43

NH3 (g)

‑11.04

‑3.976

NH3 (aq)

‑19.32

‑6.37

NH4+ (aq)

‑31.74

‑19.00

HNO3 (aq)

‑49.372

‑26.41

O2 (aq)

‑3.9

3.93

O2 (g)

0

0

OH- (aq)

‑54.957

‑37.595

H2O (g)

‑57.7979

‑54.6357

H2O (l)

‑68.3174

‑56.690

PO4-3 (aq)

-305.30

-243.50

HPO4-2 (aq)

-308.81

-260.34

H2PO4- (aq)

-309.82

-270.17

H3PO4 (aq)

-307.90

-273.08

SO4-2

‑216.90

‑177.34

HS- (aq)

‑4.22

3.01

H2S(g)

‑4.815

‑7.892

H2S(aq)

‑9.4

‑6.54