# 0.4 Acid-base equilibrium  (Page 4/7)

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We make two final notes about the results in [link] . First, it is clear the larger the value of ${K}_{a}$ , the stronger the acid. That is, when ${K}_{a}$ is a larger number, the percent ionization of the acid is larger,and vice versa. Second, the values of ${K}_{a}$ very over many orders of magnitude. As such, it is often convenient to define the quanity $p{K}_{a}$ , analogous to pH, for purposes of comparing acid strengths:

$p{K}_{a}=-\lg {K}_{a}$

The value of $p{K}_{a}$ for each acid is also listed in [link] . Note that a small value of $p{K}_{a}$ implies a large value of ${K}_{a}$ and thus a stronger acid. Weaker acids have larger values of $p{K}_{a}$ . ${K}_{a}$ and $p{K}_{a}$ thus give a simple quantitative comparison of the strength of weak acids.

## Observation 3: autoionization of water

Since we have the ability to measure pH for acid solutions, we can measure pH for pure water as well. It mightseem that this would make no sense, as we would expect $\left[{H}_{3}{O}^{+}\right]$ to equal zero exactly in pure water. Surprisingly, this is incorrect: a measurement on pure water at 25°C yields $\mathrm{pH}=7$ , so that $\left[{H}_{3}{O}^{+}\right]=1.0E-7M$ . There can be only one possible source for these ions: watermolecules. The process

${H}_{2}O\left(l\right)+{H}_{2}O\left(l\right)\to {H}_{3}{O}^{+}\left(\mathrm{aq}\right)+O{H}^{-}\left(\mathrm{aq}\right)$

is referred to as the autoionization of water. Note that, in this reaction, some water molecules behave as acid, donating protons, while otherwater molecules behave as base, accepting protons.

Since at equilibrium $\left[{H}_{3}{O}^{+}\right]=1.0E-7M$ , it must also be true that $\left[O{H}^{-}\right]=1.0E-7M$ . We can write the equilibrium constant for [link] , following our previous convention of omitting the pure water from the expression, and we find that,at 25°C,

${K}_{w}=\left[{H}_{3}{O}^{+}\right]\left[O{H}^{-}\right]=1.0E-14M$

(In this case, the subscript "w" refers to "water".)

[link] occurs in pure water but must also occur when ions are dissolved inaqueous solutions. This includes the presence of acids ionized in solution. For example, we consider a solution of 0.1M acetic acid.Measurements show that, in this solution $\left[{H}_{3}{O}^{+}\right]=1.3E-3M$ and $\left[O{H}^{-}\right]=7.7E-12M$ . We note two things from this observation: first, the value of $\left[O{H}^{-}\right]$ is considerably less than in pure water; second, the autoionization equilibrium constant remains the same at $1.0E-14$ . From these notes, we can conclude that the autoionizationequilibrium of water occurs in acid solution, but the extent of autoionization is suppressed by the presence of the acid insolution.

We consider a final note on the autoionization of water. The pH of pure water is 7 at 25°C. Adding any acidto pure water, no matter how weak the acid, must increase $\left[{H}_{3}{O}^{+}\right]$ , thus producing a pH below 7. As such, we can conclude that, for allacid solutions, pH is less than 7, or on the other hand, any solution with pH less than 7 is acidic.

## Observation 4: base ionization, neutralization and hydrolysis of salts

We have not yet examined the behavior of base molecules in solution, nor have we compared the relative strengthsof bases. We have defined a base molecule as one which accepts a positive hydrogen ion from another molecule. One of the most commonexamples is ammonia, $N{H}_{3}$ . When ammonia is dissolved in aqueous solution, the followingreaction occurs:

$N{H}_{3}\left(\mathrm{aq}\right)+{H}_{2}O\left(l\right)\to N{H}_{4}^{+}\left(\mathrm{aq}\right)+O{H}^{-}\left(\mathrm{aq}\right)$

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