The Acidity constant, pK_a and determining basicity from pK_a

Defining pK_a

In explaining how we derive pK_b it is necessary to look first at the acidity constant, pK_a.

The pK_a of an acid is the pH at the point where the acid is exactly half dissociated.

To measure the strength of an acid relative to water and determine its effectiveness as a proton donor, the equilibrium constant is used.

However as water is a constant it can be removed from the expression to give a new equilibrium constant which is the K_a.

The larger the K_a the stronger the acid whereas the smaller the K_a the weaker the acid.

You will often find K_a expressed in logarithmic form

pK_a = -log K_a

The lower the pK_a the larger the equilibrium constant K_a is and hence the stronger the acid.

Acid Strength

Most important factor in strength of an acid is the stability of the conjugate base, the more stable the conjugate base the stronger the acid. An important factor in the stability of a conjugate base is which atom possesses the negative charge, the more electronegative it is the more stable the base will be.

Conjugate Acids and Conjugate bases

The stronger the acid, HA the weaker its conjugate base H^-

The stronger the base, B the weaker its conjugate acid BH

Every base when protonated forms the conjugate acid of the particular base. The same way that every acid can be deprotonated to form its conjugate base.

Strong bases will be protonated readily to form a weak conjugate acid. This is because the strong base readily wants to accept a proton, therefore it is then reluctant to give it up, the resulting conjugate acid is very weak as this proton will not be readily lost.

Weak bases are not readily protonated therefore the resulting conjugate acid is very strong and deprotonates readily to reform the weak base, which is more stable.

This allows us to use the pK_a of conjugate acids to determine the basicity of a bases. If the pK_a of the conjugate acid is low this means it is very acidic and hence the base is weak. If the pK_a of that acid is high then the stronger the base. The higher the pK_a

Basicity

How do we measure the strength of a base based on pK_a?

For basic anions we can simply look up the pK_avalue for the neutral conjugate acid, a high pK_a means that the conjugate acid is reluctant to give up a proton hence the base is very basic.

But what if we need the basicity of a neutral base such as ammonia, the pK_a of ammonia is 33 but this gives the value for deprotonating ammonia and obtaining NH₂^-. We want the value for adding a proton to ammonia, so we look up the pK_a value of NH₄^-. This is 9.24, so we can say that the pK_aH for ammonia is 9.24.

This is illustrated even more clearly with water, as the pK_a for water is 15.74. water is the conjugate acid of the hydroxide ion, OH^-, therefore the pK_aH for OH^- is 15.74. Therefore this demonstates that OH^- is a stronger base than ammonia.

The higher the pK_aH the stronger the base.

The next page disscusses pK_b

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