# How would you find the appropriate buffer with given pKa's and a given pH?

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Feb 14, 2016

The pH of the solution should fall on the buffering range of a particular buffer solution.

#### Explanation:

Buffering range can be simply defined as the pH range wherein the solution can resists drastic changes in pH upon addition of small amounts of an acid or a base. Ideally, the buffering range of a buffer solution is equal to $p K a \pm 1$.

To illustrate how this basic rule can be applied, let's have an example. Suppose you need to prepare a buffer solution with a pH of 5.0, and in your laboratory the only available reagents are acetate buffer and phosphate buffer. The main problem now is which of these two is suitable to make the said buffer solution.

First let's determine first the components of the two possible buffers. For acetate buffer, it main component will be acetic acid $\left(C {H}_{3} C O O H\right)$ and acetate ion $\left(C {H}_{3} C O {O}^{-}\right)$. The equilibrium reaction involved in this solution will be the dissociation of acetic acid in water:

$C {H}_{3} C O O H$ $+$ ${H}_{2} O$ $r i g h t \le f t h a r p \infty n s$ $C {H}_{3} C O {O}^{-}$ $+$ ${H}_{3} {O}^{+}$

Meanwhile, the usual components of a phosphate buffer system will be ${H}_{2} P {O}_{4}^{-}$ and $H P {O}_{4}^{2 -}$. The equilibrium reaction involved in this solution will be the dissociation of ${H}_{2} P {O}_{4}^{-}$ in water:

${H}_{2} P {O}_{4}^{-}$ $+$ ${H}_{2} O$ $r i g h t \le f t h a r p \infty n s$ $H P {O}_{4}^{2 -}$ $+$ ${H}_{3} {O}^{+}$

The next step to consider in this problem will be to determine the buffering range of the two buffer systems. For acetate buffer, the pKa value of acetic acid is equal to 4.7 so that getting $p K a \pm 1$, the buffer is suitable for a pH range of $4.7 \pm 1$ or from 3.7 to 5.7.

Meanwhile for phosphate buffer, the pKa value of ${H}_{2} P {O}_{4}^{-}$ is equal to 7.2 so that the buffer system is suitable for a pH range of $7.2 \pm 1$ or from 6.2 to 8.2.

Since the target pH of the buffer to be prepared is 5.0, the best buffer system to use will be the acetate buffer since 5.0 fall in the maximum buffering range for this buffer system.

Note: To determine the pKa of the acidic component of the buffer system, usually you need to look for its acid dissociation constant. To determine the pKa, use this equation:

$p K a = - \log K a$

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