SME
Organic Chemistry II · Problem type
Percent ionized at a pH
Use this for “Benzoic acid has pKₐ 4.20. What percent is ionized at pH 3.50, and how much stronger is it than phenol (pKₐ 9.95)?”
Diagram
Since pH = −log₁₀[H⁺], here [H⁺] = 10⁻⁷·⁴⁰ = 3.9811 × 10⁻⁸ mol/L.
Above 7: basic. pOH = 14 − pH = 6.6.
This is an example. Type your own values to start a new problem.
pKₐ
Acid’s pKₐ
example
pH
pH of the solution
example
r
Ratio [A⁻] ÷ [HA]
calculated
%
Percent ionized
calculated · %
pKₐ₂
Second acid’s pKₐ
example
f
Kₐ ÷ Kₐ₂, times stronger than the second acid
calculated
Formulas
log₁₀(
r
)
=
pH
−
pKₐ
log₁₀(437) = 7.40 − 4.76
%
=
100
×
r
1 +
r
99.771
=
100
×
437
1 + 437
f
=
10
pKₐ₂ − pKₐ
1.5488 ×
10
5
=
10
9.95 − 4.76
Assumptions
•
Henderson–Hasselbalch: log([A⁻] ÷ [HA]) = pH − pKₐ, so each unit of pH above pKₐ makes the ratio 10 times larger.
•
The percent ionized is the share as A⁻: 100 × ratio ÷ (1 + ratio).
•
For an amine, use its conjugate acid’s pKₐ (the ammonium ion); the percent then reads as the neutral amine.
•
The acid’s Kₐ is 10pKₐ₂ − pKₐ times the second acid’s: a smaller pKₐ is a stronger acid.
Step-by-step
WE KNOW
pKₐ = 4.76, pH = 7.40, pKₐ₂ = 9.95
FIND
ratio [A⁻] ÷ [HA] (r), percent ionized (%), Kₐ ÷ Kₐ₂, times stronger than the second acid (f)
Step 1 · Find ratio [A⁻] ÷ [HA] (r)
Use log₁₀(r) = pH − pKₐ
Undo the log: raise 10 to pH − pKₐ.
r
=
10
pH − pKₐ
r
=
10
7.40 − 4.76
r
=
10
2.64
r
=
436.5
Step 2 · Find percent ionized (%)
Use % = 100 × r ÷ (1 + r)
For
each
1
part
HA
there
are
r
parts
A⁻,
so
A⁻
is
r
parts
of
1
+
r
.
%
=
100
×
436.5
1 + 436.5
%
=
100
×
436.5
437.5
%
=
43,650
437.5
% = 99.771% → pH is above pKₐ, so most of the acid has lost its proton.
Step 3 · Find Kₐ ÷ Kₐ₂, times stronger than the second acid (f)
Use f = 10pKₐ₂ − pKₐ
Each unit of pKₐ is a factor of 10 in Kₐ: raise 10 to the difference.
f
=
10
9.95 − 4.76
f
=
10
5.19
f
=
1.5488 ×
10
5
Check
Put the numbers back in. Both sides should match.
log₁₀(436.5) = 7.40 − 4.76 ✓
99.771
=
100
×
436.5
1 + 436.5
✓
1.5488 ×
10
5
=
10
9.95 − 4.76
✓
Topic check
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