What you are given
- pKa: 8.06
- Target pH: 8
- Total concentration: 50 mM
Formula: pH = pKa + log₁₀([A⁻]/[HA])
Buffers
How do you calculate a buffer using Henderson-Hasselbalch?
pH = pKa + log10([A-]/[HA]). Rearranged, the base to acid ratio is 10^(pH - pKa). Split the total buffer concentration in that ratio to get the amount of each component.
Worked example
Every number below is computed by the calculator, not typed in
The working
- Base : acid ratio:
r = [A⁻]/[HA] = 10^(pH − pKa) - Substitute:
r = 10^(8 − 8.06)=0.871 - Base fraction:
r / (1 + r)=0.4655 - Acid fraction:
1 / (1 + r)=0.5345 - Conjugate base [A⁻]:
C_total · r/(1+r) = 50 mM · 0.4655=23.28 mM - Weak acid [HA]:
C_total · 1/(1+r) = 50 mM · 0.5345=26.72 mM
For pH 8, combine 23.28 mM conjugate base with 26.72 mM acid.
What each symbol means
- pH: Target pH
- pKa: Acid dissociation constant (log)
- [A⁻]: Conjugate base concentration (M)
- [HA]: Weak acid concentration (M)
Source: Henderson-Hasselbalch equation. A printable one-page version is on the formula sheet.
Where this usually goes wrong
- Choosing a buffer whose pKa is more than one unit from the target pH. Outside pKa plus or minus 1 there is almost no buffering capacity left.
- Ignoring temperature. Tris shifts by about -0.028 pH units per degree C, so a buffer set at room temperature is a different pH in the cold room.
- Adjusting the pH before making up to volume, then wondering why it moved.
Try it yourself
Two problems, with the working revealed
Problem 1 Buffer / pH
Work out the conjugate base and weak acid concentrations.
- pKa: 4.76
- Target pH: 4.76
- Total concentration: 200 mM
Show the answer and the working
For pH 4.76, combine 100 mM conjugate base with 100 mM acid.
- Base : acid ratio:
r = [A⁻]/[HA] = 10^(pH − pKa) - Substitute:
r = 10^(4.76 − 4.76)=1 - Base fraction:
r / (1 + r)=0.5 - Acid fraction:
1 / (1 + r)=0.5 - Conjugate base [A⁻]:
C_total · r/(1+r) = 200 mM · 0.5=100 mM - Weak acid [HA]:
C_total · 1/(1+r) = 200 mM · 0.5=100 mM
Open this in the calculator to change the numbers.
Problem 2 Buffer / pH
Work out the conjugate base and weak acid concentrations.
- pKa: 8.06
- Target pH: 8
- Total concentration: 10 mM
Show the answer and the working
For pH 8, combine 4.655 mM conjugate base with 5.345 mM acid.
- Base : acid ratio:
r = [A⁻]/[HA] = 10^(pH − pKa) - Substitute:
r = 10^(8 − 8.06)=0.871 - Base fraction:
r / (1 + r)=0.4655 - Acid fraction:
1 / (1 + r)=0.5345 - Conjugate base [A⁻]:
C_total · r/(1+r) = 10 mM · 0.4655=4.655 mM - Weak acid [HA]:
C_total · 1/(1+r) = 10 mM · 0.5345=5.345 mM
Open this in the calculator to change the numbers.
Do it with your own numbers.
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