How to Calculate pKa Values

How to Calculate pKa Values
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In the Bronsted-Lowry formulation of acids and bases, an acid is a compound that releases a proton in solution, while a base is a compound that accepts a proton. When a Bronsted acid dissolves in a solvent, it produces a conjugate base, while at the same time the solvent acts as a base and produces a conjugate acid. Dividing the concentrations of conjugate acid and base, by the concentrations of the original compounds produces the equivalence constant Keq, which is a measure of how strong the original acid is. Chemists refer to Keq as the Ka value of the reaction when the solvent is water. This number can vary by many orders of magnitude, so to make calculations easier, chemists usually use the pKa number, which is the negative logarithm of the Ka value.

Ka Is the Strength of an Acid in Water

When a generic acid (HA) dissolves in water, it donates a proton, and the product of the reaction consists of H3O+ and A-, which is the conjugate base of the reaction. Depending on the relative abilities of HA to donate protons and A- to accept them, the reaction can also proceed in the opposite direction until eventually an equilibrium is achieved.

Chemists determine the strength of an acid (Ka) by measuring the concentrations of HA, H30+ and A- at equilibrium and dividing the concentrations of the products by the concentration of the original acid. Because the concentration of water is a constant, they leave it out of the equation.

Ka = [H3O+] [A-]/[HA]

Converting to pKa

Ka values can be very large or very small. For example, the Ka value for hydrochloric acid (HCl) is around 107, while the Ka value for ascorbic acid (vitamin C) is 1.6 X 10-12. Working with such numbers is inconvenient, so to makes things easier, chemists have defined the pKa number as:

pKa = -log Ka

According to this definition, the pKa value for hydrochloric acid is -log 107 = -7, while the pKa for ascorbic acid is -log (1.6 x 10-12) = 11.80. As is evident, the smaller the pKa number, the stronger the acid.

Finding Logarithms

A logarithm is basically the opposite of an exponent. If we have an expression such as log10x = y, we can find x by taking the exponent to the base 10 of both sides: 10log x = 10y. By definition, 10logx = x, so the expression becomes x = 10y. The pKa value is a negative logarithm, which means when the equation -log x = y is reversed, x is equal to a negative exponent 10-y, which is a small number if y is large and a large number if y is small.

In practice, finding the logarithms can be complicated, so most scientists use logarithm tables or a scientific calculator. To find a base 10 logarithm on a scientific calculator, you enter the value of the logarithm and tap the "log10" key.

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