What is the concentration of the predominant form of #"H"_3"A"# at pH 10.5?
#"p"K_1 = 9.14#
#"p"K_2 = 11.7#
#"p"K_1 = 13.8#
2 Answers
The concentration of the dominant form at pH = 10.5 is
So, you are dealing with a triprotic acid. Here are the three generic forms of the acid
The pH of the solution is
Now you have to set up a system of three equations with three unknowns - the concentrations of the acid forms. From now on, I'll use this notation for simplicity
Plugging in the pH and the two pKa values will get
Solving these two equations for
SInce we need to determine the value of
Finally, you'll get
Therefore, the concentration of
The dominant form at pH 10.5 is H₂A⁻, with a concentration of 6.9 mmol/L.
Warning: This is a very long answer, but this is a complicated problem.
We must use the systematic approach to chemical equilibrium.
H₃A ⇌ H⁺ + H₂A⁻;
H₂A⁻ ⇌ H⁺ + HA²⁻;
HA²⁻ ⇌ H⁺ + A³⁻;
H₂O = H⁺ + OH⁻;
Species:
H₃A, H₂A⁻, HA²⁻, A³⁻, H⁺, OH⁻ (6 species)
I am going to omit the charges and concentration brackets for easier typing. Only 2 significant figures are justified, but I will carry 3 to avoid round-off errors. I will round off at the end.
We can't use charge balance, because the pH is fixed.
Mass Balance:
(1)
(2)
(3)
(4)
(5)
(6)
There are six equations and six unknowns. We're in business.
SOLUTION:
From (2),
(7)
From (6),
(8)
Since the pH is between
Then, from (1),
(9)
From (3),
(10)
From (4),
(11)
From (10) and (11),
(12)
Substitute (10) and (12) in (9).
(13)
From (10),
(14)
From (12),
(15)
From (5),
(16)
In decreasing order of concentration,
[H₂A⁻] = 6.9 × 10⁻³ mol/L = 6.9 mmol/L
[OH⁻] = 3.2 × 10⁻⁴ mol/L
[H₃A] = 3.0 × 10⁻⁴ mol/L
[HA²⁻] = 4.4 × 10⁻⁵ mol/L
[A³⁻] = 2.2 × 10⁻⁸ mol/L
[H⁺] = 3.2 × 10⁻¹¹ mol/L
Check: [H₃A] + [H₂A⁻] + [HA²⁻] + [A³⁻] = (3.0 × 10⁻⁴ + 6.9 × 10⁻³ + 4.4 × 10⁻⁵ + 2.2 × 10⁻⁸) mol/L = 7.2 × 10⁻³ mol/L = 7.2 mmol/L
