# pH and pKa Relationship: The Henderson-Hasselbalch Equation

## Understand the Relationship Between pH and pKa

The pH is a measure of the concentration of hydrogen ions in an aqueous solution. pKa (acid dissociation constant) is related, but more specific, in that it helps you predict what a molecule will do at a specific pH. Essentially, pKa tells you what the pH needs to be in order for a chemical species to donate or accept a proton. The Henderson-Hasselbalch equation describes the relationship between pH and pKa.

### pH and pKa

Once you have pH or pKa values, you know certain things about a solution and how it compares with other solutions:

• The lower the pH, the higher the concentration of hydrogen ions, [H+]. The lower the pKa, the stronger the acid and the greater its ability to donate protons.
• pH depends on the concentration of the solution. This is important because it means a weak acid could actually have a lower pH than a diluted strong acid. For example, concentrated vinegar (acetic acid, which is a weak acid) could have a lower pH than a dilute solution of hydrochloric acid (a strong acid). On the other hand, the pKa value is a constant for each type of molecule. It is unaffected by concentration.
• Even a chemical ordinarily considered a base can have a pKa value because the terms "acids" and "bases" simply refer to whether a species will give up protons (acid) or remove them (base). For example, if you have a base Y with a pKa of 13, it will accept protons and form YH, but when the pH exceeds 13, YH will be deprotonated and become Y. Because Y removes protons at a pH greater than the pH of neutral water (7), it is considered a base.

### Relating pH and pKa With the Henderson-Hasselbalch Equation

If you know either pH or pKa you can solve for the other value using an approximation called the Henderson-Hasselbalch equation:

pH = pKa + log ([conjugate base]/[weak acid])
pH = pka+log ([A-]/[HA])

pH is the sum of the pKa value and the log of the concentration of the conjugate base divided by the concentration of the weak acid.

At half the equivalence point:

pH = pKa

It's worth noting sometimes this equation is written for the Ka value rather than pKa, so you should know the relationship:

pKa = -logKa

### Assumptions That Are Made for the Henderson-Hasselbalch Equation

The reason the Henderson-Hasselbalch equation is an approximation is because it takes water chemistry out of the equation. This works when water is the solvent and is present in a very large proportion to the [H+] and acid/conjugate base. You shouldn't try to apply the approximation for concentrated solutions. Use the approximation only when the following conditions are met:

• −1 < log ([A−]/[HA]) < 1
• Molarity of buffers should be 100x greater than that of the acid ionization constant Ka.
• Only use strong acids or strong bases if the pKa values fall between 5 and 9.

### Example pKa and pH Problem

Find [H+] for a solution of 0.225 M NaNO2 and 1.0 M HNO2. The Ka value (from a table) of HNO2 is 5.6 x 10-4.

pKa = −log K= −log(7.4×10−4) = 3.14

pH = pka + log ([A-]/[HA])

pH = pKa + log([NO2-]/[HNO2])

pH = 3.14 + log(1/0.225)

pH = 3.14 + 0.648 = 3.788

[H+] = 10−pH = 10−3.788 = 1.6×10−4

### pH, pKa, and Henderson-Hasselbalch Equation Key Takeaways

• The pka is the pH value at which a chemical species will accept or donate a proton.
• The lower the pKa, the stronger the acid and the greater the ability to donate a proton in aqueous solution.
• The Henderson-Hasselbalch equation relates pKa and pH. However, it is only an approximation and should not be used for concentrated solutions or for extremely low pH acids or high pH bases.

### Sources

• de Levie, Robert. (2003). "The Henderson–Hasselbalch Equation: Its History and Limitations". J. Chem. Educ. 80 (2): 146. doi:
• Hasselbalch, K. A. (1917). "Die Berechnung der Wasserstoffzahl des Blutes aus der freien und gebundenen Kohlensäure desselben, und die Sauerstoffbindung des Blutes als Funktion der Wasserstoffzahl". Biochemische Zeitschrift. 78: 112–144.
• Lawrence J. Henderson (1 May 1908). "Concerning the relationship between the strength of acids and their capacity to preserve neutrality" (Abstract). Am. J. Physiol. 21 (4): 173–179.
• Po, Henry N.; Senozan, N. M. (2001). "Henderson–Hasselbalch Equation: Its History and Limitations". J. Chem. Educ. 78 (11): 1499–1503. doi: