mathematics

Henderson–Hasselbalch equation

Henderson–Hasselbalch equation is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Henderson–Hasselbalch equation rather than just read about it. In short: In chemistry and biochemistry, the pH of weakly acidic chemical solutions can be estimated using the Henderson–Hasselbalch Equation: pH = p K a + log 10 ⁡ ( [ Base ] [ Acid ] ) {\displaystyle {\ce {pH}}={\ce {p}}K_{{\ce {a}}}+\log _{10}\left({\frac {[{\ce {Base}}]}{[{\ce {Acid}}]}}\right)} The equation relates the pH of the weak acid to the numerical value of the acid dissociation constant, Ka, of the acid, and the…

Key takeaways

Henderson–Hasselbalch equation belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Henderson–Hasselbalch equation to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Henderson–Hasselbalch equation from memory before moving on to harder problems.

Reference excerpt

In chemistry and biochemistry, the pH of weakly acidic chemical solutions can be estimated using the Henderson–Hasselbalch Equation:

pH = p K a + log 10 ⁡ ( [ Base ] [ Acid ] ) {\displaystyle {\ce {pH}}={\ce {p}}K_{{\ce {a}}}+\log _{10}\left({\frac {[{\ce {Base}}]}{[{\ce {Acid}}]}}\right)} The equation relates the pH of the weak acid to the numerical value of the acid dissociation constant, Ka, of the acid, and the ratio of the concentrations of the acid and its conjugate base. Acid-base Equilibrium Reaction

H A ( a c i d ) ⇌ A − ( b a s e ) + H + {\displaystyle \mathrm {{\underset {(acid)}{HA}}\rightleftharpoons {\underset {(base)}{A^{-}}}+H^{+}} }

The Henderson–Hasselbalch equation is often used for estimating the pH of buffer solutions by approximating the actual concentration ratio as the ratio of the analytical concentrations of the acid and of a salt, MA. It is also useful for determining the volumes of the reagents needed before preparing buffer solutions, which prevents unnecessary waste of chemical reagents that may need to be further neutralized by even more reagents before they are safe to expose. For example, the acid may be carbonic acid

CO 2 + H 2 O ⇌ H 2 CO 3 ⇌ HCO 3 − + H + {\displaystyle {\ce {CO2}}+{\ce {H2O}}\rightleftharpoons {\ce {H2CO3}}\rightleftharpoons {\ce {HCO3-}}+\mathrm {H^{+}} }

The equation can also be applied to bases by specifying the protonated form of the base as the acid. For example, with an amine, R N H 2 {\displaystyle \mathrm {RNH_{2}} }

R N H 3 + ⇌ R N H 2 + H + {\displaystyle \mathrm {RNH_{3}^{+}\rightleftharpoons RNH_{2}+H^{+}} }

The Henderson–Hasselbalch buffer system also has many natural and biological applications, from physiological processes (e.g., metabolic acidosis) to geological phenomena.

History The Henderson–Hasselbalch equation was developed by Lawrence Joseph Henderson and Karl Albert Hasselbalch. Henderson was a biological chemist and Hasselbalch was a physiologist who studied pH. In 1908, Henderson derived an equation to calculate the hydrogen ion concentration of a bicarbonate buffer solution, which rearranged looks like this:

In 1909, Sørensen introduced the pH terminology, which allowed Hasselbalch to re-express Henderson's equation in logarithmic terms, resulting in the Henderson–Hasselbalch equation.

Assumptions, limitations, and derivation A simple buffer solution consists of a solution of an acid and a salt of the conjugate base of the acid. For example, the acid may be acetic acid and the salt may be sodium acetate. The Henderson–Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant, Ka of the acid, and the concentrations of the species in solution.

To derive the equation a number of simplifying assumptions have to be made. Assumption 1: The acid, HA, is monobasic and dissociates according to the equations

HA ↽ − − ⇀ H + + A − {\displaystyle {\ce {HA <=> H^+ + A^-}}}

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Henderson–Hasselbalch equation

Start with the simplest possible case. Write down what Henderson–Hasselbalch equation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Henderson–Hasselbalch equation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Henderson–Hasselbalch equation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Henderson–Hasselbalch equation

In research: Henderson–Hasselbalch equation appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Henderson–Hasselbalch equation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Henderson–Hasselbalch equation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Acid–base chemistry, Equilibrium chemistry, Mathematics in medicine, so understanding it makes those chapters shorter.
In everyday life: Look for Henderson–Hasselbalch equation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Henderson–Hasselbalch equation” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Henderson–Hasselbalch equation in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Henderson–Hasselbalch equation means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Henderson–Hasselbalch equation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Henderson–Hasselbalch equation in simple terms?

In chemistry and biochemistry, the pH of weakly acidic chemical solutions can be estimated using the Henderson–Hasselbalch Equation: pH = p K a + log 10 ⁡ ( [ Base ] [ Acid ] ) {\displaystyle {\ce {pH}}={\ce {p}}K_{{\ce {a}}}+\log _{10}\left({\frac {[{\ce {Base}}]}{[{\ce {Acid}}]}}\right)} The equa…

Why does Henderson–Hasselbalch equation matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Henderson–Hasselbalch equation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Henderson–Hasselbalch equation.