# Calculating Percent Dissociation

#### Learning Objective

- Calculate percent dissociation for weak acids from their K
_{a}values and a given concentration.

#### Key Points

- Percent dissociation is symbolized as α (alpha) and represents the ratio of the concentration of dissociated hydrogen ion [H
^{+}] to the concentration of the undissociated species [HA]. - Unlike K
_{a}, percent dissociation varies with the concentration of HA; dilute acids dissociate more than concentrated ones. - Percent dissociation is related to the concentration of both the conjugate base and the acid's initial concentration; it can be calculated if the pH of the solution and the pKa of the acid are known.

#### Terms

- percent ionizationthe fraction of an acid that undergoes dissociation
- dissociationthe process by which compounds split into smaller constituent molecules, usually reversibly.

We have already discussed quantifying the strength of a weak acid by relating it to its acid equilibrium constant K

_{a}; now we will do so in terms of the acid's

*percent dissociation*. Percent dissociation is symbolized by the Greek letter alpha, α, and it can range from 0%< α < 100%. Strong acids have a value of α that is equal to or nearly 100%; for weak acids, however, α can vary, depending on the acid's strength.

## Example

Calculate the percent dissociation of a weak acid in a$0.060\;M$

solution of HA ($K_a=1.5\times 10^{-5}$

).To determine percent dissociation, we first need to solve for the concentration of H

^{+}. We set up our equation as follows:

$K_a=\frac{[H^+][A^-]}{[HA]}$

$1.5\times 10^{-5}=\frac{x^2}{0.060-x}$

However, because the acid dissociates only to a very slight extent, we can assume

*x*is small. The above equation simplifies to the following:

$1.5\times 10^{-5}\approx \frac{x^2}{0.060}$

$x=[H^+]=9.4\times 10^{-4}$

To find the percent dissociation, we divide the hydrogen ion's concentration of by the concentration of the undissociated species, HA, and multiply by 100%:

$\alpha = \frac{[H^+]}{[HA]}\times 100\%=\frac{9.4\times 10^{-4}}{0.060}\times 100\%=1.6\%$

As we would expect for a weak acid, the percent dissociation is quite small. However, for some weak acids, the percent dissociation can be higher—upwards of 10% or more. For example, with a problem involving the percent dissociation of a 0.100 M chloroacetic acid, we cannot assume x is small, and therefore use an ICE table to solve the problem.

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