Chemistry of Freshwaters - Principles of Environmental Chemistry - page 106

M 31 (aq) ,M(OH) 21 (aq) ,M(OH) 2 1 (aq) ,M(OH) 3 0 (aq) ,andM(OH) 4 (aq) are
the hydrolysis products for many M III cations (see Section 3.2.3.2).
M 31 (aq) is generally found at low pH and only at extremely high pH is
M(OH) 4 formed. The dependence of Cr III hydrolysis reactions on pH is
illustrated in Example 3.8.
Example 3.8: Determination of Cr III speciation in an aqueous solution at
pH 1, 6, and 11. Use { Cr III T } ¼ 10 6 mol L 1 and log*b 1 ¼ 4.00,
log*b 2 ¼ 9.62, log*b 3 ¼ 16.75, and log*b 4 ¼ 27.77. Assume that no
Cr(OH) 3 is precipitated, i.e. homogeneous solution, and that inorganic
and organic ligands are absent.
Cr 3 þ þ H 2 O Ð CrOH 2 þ þ H þ b 1
Cr 3 þ þ 2H 2 O Ð Cr ð OH Þ 2 þ 2H þ b 2
Cr 3 þ þ 3H 2 O Ð Cr ð OH Þ 3 þ 3H þ b 3
Cr 3 þ þ 4H 2 O Ð Cr ð OH Þ 4 þ 4H þ b 4
f Cr II T g¼f Cr 3 þ gþf CrOH 2 þ gþf Cr ð OH Þ 2 gþf Cr ð OH Þ 3 g
þf Cr ð OH Þ 4 g¼ 10 6 mol L 1
¼f Cr 3 þ gð 1 þ b 1 =f H þ gþ b 2 =f H þ g 2 þ b 3 =f H þ g 3
þ b 4 =f H þ g 4 Þ
This equation can be solved for {Cr 31 } at various pH values by using
the equilibrium constants for each of the four equilibria above,
e.g. at pH 2, {Cr 31 } ¼ 9.90 10 7 mol L 1 .
The concentrations of all other species can be calculated using {Cr 31 }
at each selected pH value,
e.g. at pH 2, {CrOH 21 } ¼ (*b 1 /{H 1 }) {Cr 31 } ¼ 0.01 9.90 10 7 ¼
9.90 10 9 mol L 1 .
Plotting log{}against pH illustrates that the dominant species of
Cr III are Cr 31 , Cr(OH) 2 1 , and Cr(OH) 4 at pH 1, 6, and 11,
respectively. Alternatively, the same information may be presented
in a plot of mole fraction, w, against pH. The mole fractions can be
obtained by dividing species activity by the total activity of Cr III , e.g.
w Cr31 ¼ {Cr 31 }/{Cr III T }.