## Problems

2.1 Calculate the formula weight and equivalent weight of (a) MgC03, (b) NaN03, (c) C02, and (d) K2HP04. You may have to assume a reaction to determine Z

Answer: (a) 84.3,42.15; (b) 85,85; (c) 44,22; (d) 174.2,87.1

2.2 Calculate the formula weight and equivalent weight of (a) BaS04, 0) Na2CO„ (c) H2S04, and (¿0 Mg(OH)2.

2.3 What is the molar concentration of a solution containing 10 g/L of (<z) NaOH, (i>) Na2S04, (c) K2Cr207, and {<*) KC1?

Answer: (a) 0.25 M; (b) 0.0704 M; (c) 0.034 M; (d) 0.134 M

2.4 (a) Calculate the weight of KMn04 contained in 2 liters of a 0.15 M solution. (b) Calculate the weight of KMn04 contained in 2 liters of a 0.15 N solution.

2.5 A water sample contains 44 rag/L of calcium ion and 19 mg/L of magnesium ion. What is the hardness expressed as mg/L of CaC03? Note that hardness is the sum of the multivalent cations.

2.6 A water sample contains 118 mg/L of bicarbonate ion, 19 mg/L of carbonate ion, and has a pH of 9.5. What is the alkalinity of this water expressed as mg/L of CaC03? Note that alkalinity (Alk) is sometimes defined by the following expression: eq/L of Alk = [HCOH + 2[COn + [OH"] - [H+J where [ ] represents concentration in mol/L.

2.7 Balance the following equations:

(c) Mn02 + NaCl + H2S04 -> MnS04 + H20 + Cl2 + Na,SO„

{d Ca(H2P04)2 + NaHCOj -> CaHP04 + Na2HP04 + H20 + C02

2.8 Balance the following equations:

(c) FeS04 + K2Cr207 + H2S04 Fe2(S04)3 + Cr2(S04)3 + K2SO, + HsO (rf) A12(S04)3 • 14 H20 + Ca(HCOj)2 -> Al(OH)3 + CaS04 + H20 + C02

2 9 Baiance the following equations:

(c) H2CA + KMn04 + H2SO„ C02 + MnS04 + K2S04 + H20

(d) SOf" + Pe3+ + H20 ->• SO;" + Fe2+ + H* 2 10 Balance the following equations:

211 Using half reactions, write complete balanced oxidation-reduction equations for the following:

(a) Oxidation of I" to I2 and reduction of Mn02 to Mn2+ (t) Oxidation of S2Ol~ to SO'" and reduction of Cl2 to CI"

(c) Oxidation of NH4 to NO3 and reduction of 02 to H20

(d) Oxidation of CH3COO" to C02 and reduction of Cr20?" to Cr3+

(e) Oxidation of CSH,A t(> C02 and reduction of N03~ to N2

(d) 3CH3COO" + 4Cr20?" + 35H+ -> 6C02 + »Cr3-" + 22H20

(e) 5c6h,206 + 24n03" + 24h+ -> 30c02 + 12n2 + 42h,0

2.12 Using half reactions, write complete balanced oxidation-reduction equations for the following:

(a) Oxidation of Mn2+ to Mn02 and reduction of 02 to H20

(b) Oxidation of S20|" to S04~ and reduction of I2 to I"

(c) Oxidation of Nfltf to NOf and reduction of 02 to H,0

(d) Oxidation of C6H,A to C02 and reduction of Cr20*~ to Cr3+ (.&) Oxidation of CH3COO" to C02 and reduction of S04~ to H2S

2.13 Construct half reactions for the following reductions:

(c) CHjCOO" to CH3CH2CH2COO™

(c) ICHjCOO" + jH+ + «" = |CH3CH2CH2COO" + |H20

2.14 Construct half reactions for the following reductions: (c) C02 to CH4

(c) CHJCOO" + C02 to CH3CH2C00"

2.15 Develop the appropriate half reactions, and from these construct the complete oxidation-redaction equation for oxidation of H2S to S and reduction of Fe3+ to Fe2+.

2.16 Develop the appropriate half reactions, and from these construct the complete oxidation-reduction equation for oxidation of CH3CH2OH to C02 and reduction of N03 to N02.

2.17 How many moles of H2SO„ are required to form 65 g of CaS04 from CaC03?

2.18 How many grams of iodine (I2) are formed from the oxidation of an excess of KI by 6 g of K2Cr207, under acid conditions [see Bq. (2.9)]?

2.19 Calculate the volume in cubic feet occupied by 120 ib of carbon dioxide at 1.5 atm and 40°C.

2.20 Determine the weight in grams of oxygen contained in a 10-liter volume under a pressure of 5 atm and at a temperature of 0°C.

2.21 What volume of oxygen at 25°C and 0.21 atm is required for combustion of 25 g of methane gas?

2.22 If 6 g of ethane gas (CH3CH3) is burned in oxygen, {a) how many moles of water are formed; (&) how many moles of carbon dioxide are formed; (c) what is the volume in liters of carbon dioxide formed at 1 atm pressure and 20°C?

2.23 A gas mixture at 25°C and 1 atm contains 100 mg/L of H2S gas. What is the partial pressure exerted by this gas?

2.24 A 30-liter volume of gas at 25°C contains 12 g of methane, 1 g of nitrogen, and 15 g of carbon dioxide. Calculate (a) the moles of each gas present, (b) the partial pressure exerted by each gas, (c) the total pressure exerted by the mixture, and (d) the percentage by volume of each gas in the mixture.

2.25 Five liters of water are equilibrated with a gas mixture containing carbon dioxide at a partial pressure of 0.3 atm. If the Henry's law constant for carbon dioxide solubility is 31.6 atm-L/mol, at 25°C how many grams of carbon dioxide are dissolved in the water?

2.26 What is the concentration of oxygen dissolved in water at 20°C in equilibrium with à gas mixture at 0.81 atm and containing 21 percent by volume of oxygen?

2.27 A non-aqueous-phase liquid (NAPL) mixture contains 100 kg of tetrachloroethene (C2C14; also called perchloroethene (PCE)], 100 kg of benzene (CSH6), 100 kg of toluene (C,HS), 80 kg of ethylbenzene (C8H10), and 60 kg of xylene (CsHt0). Calculate the mole fraction of each compound in the NAPL.

2.28 Consider an NAPL mixture of tetrachloroethene (PCE) and fuel containing BTEX (benzene, toluene, ethylbenzene, and xylene) with the following mole fractions: PCE = 0.10, B = 0.15, T = 0.15, E = 0.08, and X = 0.10. The vapor pressures (in atmospheres at 25°C) of the pure compounds'0 are PCE = 0.0251 B = 0.126, T = 0.0380, E = 0.0126, and X = 0.0117, and Henry's constant K„ (in atm-L/mol at 25°C) for PCE is 26.9.

l0Schwarzenbach, Gschwend, and Imboden, "Environmental Organic Chemistry," Wiley, New York, 1993.

(a) Assuming Raoult's and Henry's laws apply, estimate the aqueous concentration of PCE in water that is in equilibrium with this NAPL mixture.

(b) Estimate the reduction in aqueous PCE concentration (solubility) due to the presence of BTEX. Him: First estimate the solubility when PCE is the sole NAPL (mole fraction = 1,0).

2.29 The aqueous concentration of trichloroethene (TCE) is measured to be 20 mg/L. The water (T = 25°C) is in contact with a dense non-aqueous-phase liquid (DNAPL) containing TCE. Assuming Henry's and Raoult's laws hold, estimate the mole fraction of TCE in the DNAPL. At 25°C, Henry's constant for TCE is 11.6 atm-L/mol and the vapor pressure of pure TCE is 0.0977 atm."

2.30 Calculate the percent ionization and hydrogen ion concentration at 25°C in a solution containing (a) 0.10 M H2C03, and (b) 0.01 M H2C03.

Answer: (a) 0.211 percent, 2.11 X 10*" mol/L; (f>) 0.67 percent, 6.67 X 10"5 mol/L

2.31 Calculate the percent ionization and hydrogen ion concentration in a solution containing 0.05 M hypochlorous acid (HOC!), which has an ionization constant at 25°C of 2.9 X 10~8.

2.32 (a) Write reactions and equilibrium relationships for the first four complexes formed between cadmium(II) and chloride.

Cb) Write the equilibrium relationship for the instability constant for CdCIj".

2.33 (a) Write reactions and equilibrium relationships for the first five complexes formed between copper(II) and NH3. A sixth complex is theoretically possible, but its formation has not yet been detected.

(2>) Write the overall reaction and equilibrium relationship for the fourth complex between copper(II) and NH3.

2.34 Equilibrium constants for the complexes between cadmium(II) and chloride are Ks = 100, K2 = 4.0, K3 = 0.63, and iC, = 0.20. Calculate the molar concentration of each of the first four cadmium chloride complexes in a water sample if Cd2+ = 10"8 M and CI" = 10~3 M. Identify the most prevalent cadmium species.

Answer: 1 X 10"9,4 X 10"'2,2.52 X 10"!i, 5.04 X 10~'9, Cd2+

2.35 Do Prob. 2.34, but assume that the chloride concentration is similar to that of seawater or about 0.5 M.

2.36 Cadmium (Cd) is reported to be much more toxic as the free metal (Cd2+) than when complexed with ligands. The total soluble Cd concentration (Cr,c<l = [Cd2+] 4- the sum of all soluble Cd complexes) in a water is measured to be 10"* M. In order to ensure that the toxicity of Cd is small, it is desirable to have Cd2* be less than 10*~7 M. An environmental engineer suggests adding 0.5 M NaCl to complex the Cd2+. Ignore activity corrections and the formation of any solids. Consider only the complexes of chloride with cadmium—there are 4 (log ft = 2.0, log ft = 2.6, log ft = 2.4, and log ft = 1.7).

"Ibid.

2 37 Calculate the concentration in (a) moles per liter, {b) milligrams per liter, and (c)

number of ions per liter, for the sulfate ion in a saturated solution of barium sulfate to which barium chloride is added until [Ba2+] = 0.0001 M.

Answer (a) 10"* mol/L; (b) 0.096 mg/L; (c) 6.02 X 10" wns/L

2 38 Calculate the concentration in (a) moles per liter, (b) milligrams per liter, and (c)

number of ions per liter, for the chloride ion in a saturated solution ot silver chlonde to which silver nitrate is added until [Ag+] = 0.0001 M. 2 39 (a) Write the expression for the solubility-product constant of (1) AgCl, (2) CuS (3) MgNH4P04, (4) Au(OH)3, (5) A&QO* and (6) BaC03. <») What ions can be added to solutions containing the compounds listed in (a) which, in each case, will lower the concentration of the cation? Explain why. 2.40 Why does solubility often increase as still larger quantities of a common ion are added?

2 41 Tell what is meant by (a) common ion effect, (i>) complex ion, (c) solubility-product constant, (J) amphoteric hydroxide, (e) diverse ion effect, (f) heterogeneous equilibrium, (g) homogeneous equilibrium, (h) driving reaction to completion, and (0

saturated solution.

2.42 From each of the following values of water solubility evaluate the contending ^ solubility-product constant: (u) Mfe(P04)2l 6.1 X 10~3 mol/L, <«FeS 6.3 X 10 mol/L, (c) Zn3(P04)2,1.6 X 10~7 mol/L, and (d) CuF2,7.4 X 10"3 mol/L.

2.43 Which is the better chemical for removing calcium ions from solution, sodium hydroxide or sodium carbonate? Why?

2.44 Which is the better chemical for removing magnesium ions from solution, sodium hydroxide or sodium carbonate? Why?

2 45 Which of the following is the better chemical for removing calcium ions from water? Make sure you show the calculations necessary to justify your answer. For this problem, ignore calcium complexes.

2 46 Given the reaction NH3 + H20 ^ NH4+ + OH", how many ways can you think of or forcing the reaction („) to the right? (b) to the left? CO Under what conditions might it go to completion in either direction? 2.47 Determine how many milligrams per liter of magnesium ion will dissolve in water which is (a) 10'5 M in OH"*, (b) 10 J M in OH". 2 48 A metal-plating waste contains 20 mg/L Cu2+, and it is desired to add Ca(OH)2 to precipitate all but 0.5 mg/L of the copper. To what concentration in motes per liter must the hydroxide concentration be raised to accomplish this? Answer: 1.6 X 10"7 mol/L 2.49 A waste contains 50 mg/L of Zn» How high must the pH be raised to precipitate all but 1 mg/L of the zinc? What adverse effect might occur if the pH were raised too

2 50 Calculate the pH required to decrease the iron concentration in a water supply to 0.03

mg/L if (a) the iron is in the Fe2+ form, (b) the iron is in the Fe form.

2_5i Calculate the pH required to decrease the manganese concentration in a water supply to 0.01 mg/L if (a) the manganese is in the Mn2+ form, (b) the manganese is in the Mn3+ form.

2.52 It is desired to fluoridate a water supply by adding sufficient sodium fluoride to increase the fluoride concentration to 1 mg/L. Will this fluoride concentration be soluble in a water supply containing 200 mg/L of calcium? Show your computations.

2.53 At what Ca2+ concentration in milligrams per liter will precipitation of Ca3(P04)2 occur in a solution containing 10~6 M PO|~?

2.54 If the CO2" concentration in a water sample is 100 mg/L, what is the maximum soiubility in milligrams per liter of (a) Ca2+? (b) Mg2+?

2.55 (a) If excess AgCl is mixed in distilled water, what will be the concentration of silver in solution in milligrams per liter at equilibrium? (b) If ammonium hydroxide is added to the solution in (a) so that the resultant NH3 concentration is 0.01 mol/L, what will the total concentration of silver in solution then be? Assume if in Eq. (2.63) is equal to 5X 10~3.

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