# Calculating Buffer Capacity

I completed a titration of Ammonium Acetate buffer solution and to it I added $$\pu{2M}$$ Hydrochloric Acid.

I measured the initial $$\ce{pH}$$ of the buffer solution before any acid was added and I used methyl orange as an indicator which has a $$\mathrm{p}K_\mathrm{a}$$ value of 3. My independent variable was the temperature of the buffer.

I was just wondering how I would calculate the buffer capacity. Is it $$\Delta\ce{pH}$$/Volume?

As far as I can remember from my tutorials, the formula was $$\beta =\frac{n(\ce{H+})}{\Delta\ce{pH}},$$ meaning: How many protons have to be added to produce a change in the pH of one unit. But there might be different definitions. The IUPAC does not provide an official one.
Perhaps a derivation of the definition I was taught. Consider the Henderson-Hasselbalch equation: $$pH=pK_a+\log\bigg(\frac{[A^-]}{[HA]}\bigg).$$ Given the definition provided by Klaus above and the fact that a weak acid's $pK_a$ is unique, the only term that could possible alter the $pH$ by an amount of $\pm1$ is $\log\big(\frac{[A^-]}{[HA]}\big).$ We decide to choose the case of the $pH$ increasing by $+1$ (it does not matter which direction---either more acidic or more basic---the reaction proceeds, we simply want the magnitude of the numerical change to be 1). If the $pH$ increases by 1, then the solution becomes more basic. Consequently, the term $\log\big(\frac{[A^-]}{[HA]}\big)$ changes by $\log\big(\frac{[A^-]+\beta}{[HA]-\beta}\big)$, where $\beta$ denotes the buffer capacity. We know this term must equal $+1$ because a perfect buffer has equimolar solutions of $[HA]$ and $[A^-]$. We obtain the following equation: $$1=\log\bigg(\frac{[A^-]+\beta}{[HA]-\beta}\bigg).$$ Solving for $\beta$ yields the buffer capacity equation $$\beta=\frac{10[HA]-[A^-]}{11}.$$