192 Acid-Base Chemistry

Thus

Silica in the form of H3Si04- = a,CT,si = 0.58 x 1.33 x 10"

= 0.77 X 10" eq/liter

Alkalinity due to silicate = 0.77 x 10" eq/liter

'0.77 X 10"^ -i' X 100= 19.2 percent 4 X 10"

Alkalinity due to hydroxide = 0.44 x 10" eq/liter

0.44 X 10"\ ^ ^ jQ-4 I X 100= 11.0percent

Alkalinity due to carbonate and bicarbonate =100-(19.2 -1-11.0) = 69.8 percent

Therefore, in this water a significant fraction of the total alkalinity (almost 20 percent) is due to the silicate system.

Many interesting aspects of the carbonate system occur i n connection with heterogeneous systems containing carbonate solids and soluble :arbonate complexes. These topics are dealt w i t h i n the next two chapters.

1.14. PROBLEMS

1. Calculate the pH of the following perchloric acid, HCIO4, solutions--'' (a) 10- M.

(b) 10-« M. • t

2. Calculate the pH of the following potassium hydroxide, KOH, solutions: . (a) 10" M.

(b) 10-5 M.

3. Arsenious acid is a weak acid

HASO2 ^ H+ -h AsO^-; K, = 1 0 ' "

If 10" moles of the herbicide NaAsOz, are added to 1 liter of distilled water at 25°C, what is the resulting pH? Determine by solving the appropriate set of equations analytically^

I . (a) A solution of 10"= mole of sodium propionate (CHaCHpCOO Na) is added to 1 liter of distilled water. If the pK, = 4.87 for propionic acid, what is the solution pH? Solve the appropriate set of equations analytically and graphically and compare the results,

(b) Propionic acid is a common constituent of anaerobic digesters. If the pH of the digester contents is 7.6, what percentage of the total amount of propionic acid is ionized at 25°C?

Aqueous free chlorine is hypochlorous acid, HOCl, and hypochlorite ion, OCl , -with the relative amounts depending on the pH of the solution.

Problems 193

(a) Given that pK, = 7.5 for HOCl at 25°C, what is the pH of a solution prepared by adding 10 ^ mole of NaOCl to 1 liter of water?

(b) What is the pH at which 50 percent of the total free chlorine is present as HOCl?

(c) What is the pK^ for OCl and to what reaction does this constant apply? Neglect ionic strength effects; temperature = 25°C.

6. A solution of 10" mole of Na2HP04 is added to 1 liter of solution. (a) Write the mass balances for Na and PO4, Cr.Na. andCr.POi •

(b) Write the proton condition. (c) Write the charge balance.

7. What pH results when 10" mole of NaH2P04 are added to 1 liter of distilled water? The temperature = 25°C; assume that fi = 10" after the addition. Compare the value obtained when ionic strength effects are taken into account with that calculated when it is neglected. (See Fig. 3-4 for activity coefficients.)

8. What is the pH of a solution that is prepared by adding 10 ^ mole of HaiCO, to 1 liter of water? The temperature = 15°C; /j. = 0. (See Tables 4-2 and 4-7 for equilibrium constants.) Compare this value with that obtained if the temperature is 25°C.

9. What is the pH of a 10' M K H S O 4 solution at 25°C; M = 0?

10. Using either the table or the equations in Appendix 1, calculate (a) ao and a, for hydrofluoric acid, HF, at pH 4.2. (b) ao. «i. and for H2COI at pH 6.6. [Include both approximate (±0.05) and

exact values.] (c) ao, a,, aj, and 03 for H3PO4 at pH 8.0. Assume that activity effects are

negligible and the temperature is 25°C.

11. Calculate the a values as required in Problem 4-10 given that the ionic strength is 0.01.

12. 2.5 X 10-' mole of NHj.^,, and 2.5 x 10"' mole NaOH are added to 1 liter of distilled water at 25°C. What is the pH if = 0?

13. IQ-^ moles NH4AC and 10 ^ moles NaOH are added to 1 liter of water at 25°C. What is the pH if /x = 0?

14. What is the pH of a 25°C solution containing 10" moles NaHCOj and 2 x 10"' mole NH3 per liter if /x = 10" ?

15. A nitric acid solution, pH = 2.7, results from NO, removal from a stack gas. Neglect ionic strength effects and the temperature is 25°C. (a) How much NojCOa must be added to neutralize this solution prior to

discharge? (The final pH is 8.3. Assume that no weak acids are present in the scrubber water.) Hint: What is the predominant carbonate species at pH 8.3?

(b) What is the buffer intensity of the final solution?

194 Acid-Base Chemistry

16. How much soda ash, NapCOa, in moles/liter is required to neutralize a pickle liquor solution containing 10" mole H2S04/liter? Assume that the H2SO4 w i l l react only with the NazCOa and that the pH after neutralization is 8.3.

17. An experiment is to be conducted on breakpoint chlorination (the oxidation of ammonia by chlorine) in which it is desired to maintain the pH constant within 0.5 units of the initial pH of 8. Make the assumption that al l of the ammonia is in the NH4+ form (a reasonable assumption, since the pK, of NH4+ is 9.3 and the pH of interest is pH 8). The breakpoint reaction between CI2 and NH3 proceeds as follows:

3CI2 + 2NH4+ ^N2,9 , + 8H+ + 6C1-

The maximum amount of ammonia that w i l l be used in the experiments is 12.5 mg as N/liter (0.89 x 10" moles/liter). Select an appropriate acid-conjugate base pair and determine the concentration of it that w i l l control the pH to within 0.5 units of 8.0 during the reaction. Neglect ionic strength effects; the temperature = 25°C. Determine the buffer intensity of this solution. {Note: There is a detailed discussion of the breakpoint chlorination reaction in Chapter 7.)

1 ^ An industrial wastewater is to be discharged to a receiving stream with a pH of 8.3 and a total alkalinity = 2 x 10" eq/liter. The wastewater contains 5 X 10" M H2SO4, and the pH of the stream should not be permitted to drop below 6.3. (p) What is the maximum dilution ratio (volume waste/volume stream water)

that can be used for discharge of the wastewater? (b) What is the buffer intensity of the solution at pH 6.3?

19. A sample of natural water contains 1 x 10" M CO^^ and 3 x 10" M HCOj-. (a) As the pH is lowered during the alkalinity titration, at what pH is the C O 2

in solution in equilibrium with atmospheric C O 2 ? (b) What is the pH of the total alkalinity equivalence point, pHco^? (Neglect

dilution effects.) Give your answer to nearest 0.1 pH unit. (c) If 50 percent of the C O 2 formed during the titration "escapes," what is the

"new" pH of the total alkalinity equivalence point?

^ A sample of\natural water that has been equilibrated with CaCOais, is isolated from its surroundings. Indicate whether the addition of small quantities of the following wi l l increase, decrease, or have no effect on the total alkalinity or total acidity and state very briefly why. Neglect ionic strength effects. (a) HCl. ^ ('b) FeCla. (c) Na2S04. (d) C O 2 . ' (e) Na2C03. •• >

21. A natural water has the following partiai analysis:

pH = 8.3 [Ca2+] = 5 x 10" M [ H C O 3 - ] = 3 X 10-3 ^ []y[g2+j ^ J ^ 10-4

• [CO2, , , , ] = 3 X 10-= M [S04=-] = 1 X 10" M

Additional Readings 1

(a) What volume of O.O2NH2SO4 is required to titrate a 100-ml sample to tl total alkalinity endpoint? What is the total alkalinity in eq/liter and mg/liter as CaCOj?

(b) A waste containing 10^ moles NaOH/liter is to be discharged to th water. The pH cannot be raised above 9.5. What is the maximum numb of liters of waste that can be added to each liter of the natural wate

22. A partial water analysis is given as follows:

C O 2 = 44 mg/liter [CI"] = 1 x 10- M [ H C O 3 ] = 2 x 10-3 M [SO4 ' - ] = 1 x 10" M

(a) What is the solution pH and CO^^' concentration? (b) What is the caustic, carbonate, and total alkalinity (in eq/liter and in m

liter as CaC03)? (c) What is the mineral, C O 2 , and total acidity (in eq/liter)? (d) What is the pH if 5 x 10" mole OH" (as NaOH) are added per liter of t

above sample?

23^^^ifty ml of a natural water sample is titrated with 0.02 N H2SO4. The titro volume required to titrate to pH 8.3 is 6 ml and an additional 8 ml is requir to'titrate to pH 4.3. (a) What is the caustic, carbonate, and total alkalinity in meq/liter? (b) What is the mineral, C O 2 , and total acidity in meq/liter?

.(c) What is CT.C03?

(d) What is pHco^ and pHcoj (to the nearest 0.1 pH unit)? (e) What is [H+], [OH~], [ C O 3 ' - ] , [ H C O 3 - ] and [HjCO^] in the original sampl

Calculate using both the approximate method described in Section 4.i; and the exact procedure and compare the results.

24. A solution has a carbonate alkalinity of 1 meq/liter and a total alkalinity 6 meq/liter. The ionic strength of the solution is 10 ^ M and the temperati is 40°C. Calculate [H+], [ H C O 3 - ] , and [ C O j ' ] neglecting ionic strength effe( and compare with the values obtained when corrections are made for ioi strength effects. Use the constants given in Tables 4-2 and 4-7 for yc calculations.

25^ In some regions carbonate-bearing minerals are lacking in the earth and t ^ lakes in these regions have a low alkalinity. Acid rains, resulting fr<

conversion of industrial SO2 emissions to H2SO4, can cause significant depressions in such lakes and may result in fish kills. What volume of a< rain, pH = 4.0, is required to lower the pH of a lake to 6.7? The lake ha: volume of 20 x 10 ft^, a pH = 7.0, and an alkalinity of 30 mg/liter as CaCC

4.15. ADDITIONAL READING