Solution
1. By definition, using Eq. 2-2, the mole fraction of Ca2+ is as follows.
n 2+
x Ca2+ Ca
n 2+ n 2+ n + n + nHCO - n 2- n - n -
Ca Mg Na K 3 SO 4 Cl NO3
2. Substituting in the MW for each of the constituents yields the following:
40.08
xCa2+
40.08 24.31 22.99 39.1 61 96 35.45 62
40.08
0.11
380.93
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+
xMg2+ Mg
n 2+ n 2+ n + n + nHCO - n 2- n - n -
Ca Mg Na K 3 SO 4 Cl NO3
2. Substituting in the MW for each of the constituents yields the following:
PROBLEM 2-3
Problem Statement - Determine the mole fraction of sulfate (SO42–) for the water given
in Problem 2-1.
Solution
1. By definition, using Eq. 2-2, the mole fraction of SO2-4 is as follows:
n 2-
x SO2- SO4
4 n
Ca
2+ nMg2+ nNa+ nK+ nHCO - nCl- nNO -
3 3
2. Substituting in the MW for each of the constituents yields the following:
96
xSO2-
4 40.08 24.31 22.99 39.1 61 96 35.45 62
96
0.25
280.93
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.
mass of solute, g
M, mole/L
molecular weight of solute, g/molevolume of solution, L
0.951.85
M, mole/L 0.0179 mole/L
98 1
1. Use Eq. 2-2 to determine the mole fraction.
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