### 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