# Strengths of Acids and Bases

### Ionization Constants

The ionization constant is the ratio of concentration of products to reactants at equilibrium and can be used to calculate the strength, or measure of concentration, of an acid or base.

The strength of an acid or base depends on what fraction of it dissociates, or ionizes, usually in water. A strong acid or base, such as HCl or NaOH, completely dissociates in water and has a pH close to one end of the spectrum. In a solution containing a weak acid or base, only a fraction of the molecules dissociates, resulting in a low concentration of H+ or OH ions and a pH closer to the middle of the range.

Each acid and base has an ionization constant (Ka for acids, Kb for bases) that represents the ratio of concentration of products to reactants at equilibrium. It can be used to calculate the strength of an acid or a base.

For strong acids, ${\rm{HA}}(aq)+{\rm{H_2O}}(l)\rightarrow{\rm{A}^{-}}(aq)+{\rm{H_3O^+}}(aq)$, where HA is the undissociated acid, A is the acid's conjugate base, and H3O+ is the hydronium ion.
$K_{\rm{a}}=\frac{{[{{{\rm{H}}_{3}}{\rm{O}}^{+}}}][{\rm{A}^{-}}]}{{[{\rm{HA}}]}}$
For bases, ${\rm {H_2}\rm {O}}(l)+{\rm B^-}(aq)\rightarrow{\rm{OH^-}}(aq)+{\rm{HB}}(aq)$, where HB is the undissociated base, OH is the hydroxide ion, and B+ is the base's conjugate acid.
$K_{\rm {b}}=\frac{\lbrack\rm{OH}^{-}\rbrack\lbrack\rm{HB}^{+}\rbrack}{\lbrack{\rm B}\rbrack}$
The stronger the acid or base, the greater the numerator will be in this ratio (for Ka and Kb expressions), and therefore the greater the value of K. Note that the value of K includes ×10x.
The ionization constant can be used to calculate the concentration of each ion at equilibrium by setting the change in concentration of the initial acid or base to x and creating an initial, change, equilibrium (ICE) concentration table.
Step-By-Step Example
Using the Ionization Constant to Determine the Concentration of an Acid
Find the concentration of H+ ions in 0.20 M CH3COOH (acetic acid), $K_{a}=1.77\times10^{-5}$.
Step 1
Develop an ICE table showing how the concentration changes.
Step 2
Write the equilibrium constant in terms of x. It is clear that compared to x2, the value of x is so small that it will have a negligible impact on the equilibrium concentration of CH3COOH. Therefore, it can be ignored, and an approximation for the calculation can be used.
\begin{aligned}K_{\rm{a}}&=\frac{[\rm{H}^{+}][\rm{A}^{-}]}{[\rm{HA}]}\\&=\frac{(x)(x)}{(0.20-x)}\\&\approx\frac{x^{2}}{0.20}\end{aligned}

Step 3
Substitute the given value of the equilibrium constant.
$\frac{x^{2}}{0.20}=K_{\rm{a}}=1.77\times10^{-5}$
Solution
Rearrange the equation to isolate the variable, and then solve for x.
\begin{aligned}{x^{2}}&=(1.77\times10^{-5})(0.20)\\{x^{2}}&=3.54\times10^{-6}\\x&=\sqrt{3.54\times10^{-6}}\\&=1.9\times10^{-3}\end{aligned}
${\rm{[H}^{+}]}=x$ , so the concentration of H+ ions in 0.20 M CH3COOH is $1.9\times10^{-3}$.

### Acid-Base Strength and Molecular Structure

The molecular structure of an acid or base plays a role in determining its ionization potential (how likely it is to ionize in water), and therefore its strength.

The likelihood of an acid or base to ionize in water is determined by the strength of the bonds in the molecule and the arrangement of electronegativity among the atoms.

The strength of an acid arises from its ability to lose a proton, in other words, to break the bond between a hydrogen atom and another atom. The more unequally the electron is shared in the bond, the more likely the bond is to break. When hydrogen is bonded to a highly electronegative atom such as chlorine, the electron density becomes much greater around the electronegative atom, weakening the bond and making it easier for the proton to escape. This phenomenon explains the strength of acids such as HCl and HBr. An oxygen bonded to a hydrogen will produce a strong acid, and the more oxygens present, the stronger the acid.

#### Perchloric Acid

The strength of a base is similarly related to the electronegativity within the molecule, although because a base is a proton acceptor, its strength comes from its ability to attract and retain protons. Again, electronegativity plays an important role. In addition, for a molecule to be a base, it must have electrons to share with the proton. In ammonia, for example, the lone pair on the nitrogen is strong enough to draw a proton in and create a positively charged ammonium ion. Similarly, the oxygen in an OH ion has an extra electron, giving it a negative charge and making it a strong proton acceptor.