Solution manual for.pdf

Solution manual PROBLEM 2-1 Problem Statement - Given the following test results, determine the mole fraction of calcium (Ca2+). Concentration, Concentration, Cation mg/L Anion mg/L Ca2+ 40.0 HCO – 3 91.5 Mg2+ 12.2 2– SO4 72 Na+ 15.1 Cl– 22.9 K + 5.1 – NO3 5.0 Solution 1. By definition, using Eq. 2-2, the mole fraction of Ca2+ is as follows. n 2+ x  Ca Ca2+ n 2+  n 2+  n +  n + HCO  n 2-  n -  n - 3 4 3 2. Substituting in the MW for each of the constituents yields the following: xCa 2+  40.08 40.08  24.31 22.99  39.1 61 96  35.45  62  40.08 380.93  0.11 PROBLEM 2-2 Problem Statement - Determine the mole fraction of magnesium (Mg2+) for the water given in Problem 2-1. Solution 1. By definition, using Eq. 2-2, the mole fraction of Mg2+ is as follows. n 2+ xMg 2+  n 2+  n 2+  n +  n + Mg HCO  n 2-  n -  n - 3 4 3 2. Substituting in the MW for each of the constituents yields the following: 4 4 4 Ca Mg Na K  n - Cl NO 4    xMg 2+  24.31 40.08  24.31 22.99  39.1 61 96  35.45  62  24.31 380.93  0.06 PROBLEM 2-3 Problem Statement - Determine the mole fraction of sulfate (SO 2– ) for the water given in Problem 2-1. Solution 1. By definition, using Eq. 2-2, the mole fraction of SO2- is as follows: n 2- x  SO4 SO2- n 2+  n 2+  n +  n + HCO  n -  n - 3 3 2. Substituting in the MW for each of the constituents yields the following: xSO2-  96 40.08  24.31 22.99  39.1 61 96  35.45  62  96 280.93  0.25 PROBLEM 2-4 Problem Statement - Commercial-grade sulfuric acid is about 95 percent H2SO4 by mass. If the specific gravity is 1.85, determine the molarity, mole fraction, and normality of the sulfuric acid. Use Eq. 2-4 to determine molarity. M, mole/L  mass of solute, g molecular weight of solute, g/molevolume of solution, L 0.951.85 M, mole/L   0.0179 mole/L 98 1 1. Use Eq. 2-2 to determine the mole fraction. 2 4    I0 0 xH2SO4  n nH SO  n H2O H2SO4  98 18  98  0.84 2. Use Eq. 2-6 to determine the normality. N, eq/L  mass of solute, g equivalent weight of solute, g/eqvolume of solution, L 0.951.85 N, eq/L   0.036 eq/L 49 1 PROBLEM 2-5 Problem Statement - If the UV intensity measured at the surface of a water sample is 180 mW/cm2 , estimate the average intensity in a petri dish with an average depth of 15 mm (used to study the inactivation of microorganisms after exposure to UV light, as discussed in Chap. 13). Assume the absorptivity of the water, kA() at  = 254 nm, is 0.10 cm–1 and that the following form of the Beer–Lambert law applies: ln  I   2.303k ()x   A   Solution 1. The variables for the Beer-Lambert law are the following: I = unknown I0 = 180 mJ/cm2 kA(λ) = 0.10/cm x = 1.5 cm 2. Rearrange the Beer-Lambert law given in the problem statement to solve for I as follows: I  I e -2.303kλA x  I  280e-2.3030.101.5 I  174 mJ/cm2