# A Simple Method That Shows You How to Convert pKa to Ka Easily

The term 'pKa' is more commonly used in chemical calculations as compared to 'Ka'. Despite this, there is a lot of confusion between the two concepts. This ScienceStruck post tells you how to convert pKa to Ka, with the help of an equation relating the two values.

ScienceStruck Staff

Last Updated: Jul 16, 2017

Did You Know?

Despite the general notion that only strong acids can burn the skin, strong bases also have the same effect. Moreover, acids and bases always neutralize each other.

While pH is a popular value used to indicate the number of protons that are produced by a substance, there are other quantities, like K

_{a}, K

_{b}, pK

_{a}, and pK

_{b}, used to explain the strength of these substances. They are commonly used by chemists to decide the strength of chemical reactants in laboratories, and by pharmacists to understand the dosage of drugs. However, these values can only be used for Brønsted acids and bases, i.e., those substances which give or accept protons. This is because, other theories, like the Lewis Theory, define acids and bases in terms of electron transfers, so values like K

_{a}and pK

_{a}, which deal with protons, lose their relevance. The following sections describe the conversion of the pK

_{a}value of an acid to its K

_{a}value.

What is Kₐ?

K

_{a}is known as the 'acid dissociation constant'. When an acid is dissolved in water, its molecules split up into different ions (atoms with positive or negative charges)._{a}) tells us whether an acid is strong or weak. Let 'HA' be a molecule of an acid in an aqueous solution.Then it dissociates into ions, as given below.

HA (acid) ⇋ H

^{+}(proton) + A

^{-}(conjugate base)

The value of K

_{a}for this acid is given by the following equation.

K

_{a}= [H

^{+}][A

^{-}] ÷ [HA]

If the value of K

_{a}is high, then the acid is strong, since the numerator (concentration of ions) in the equation is high. If the value of K

_{a}is low, this means the denominator (concentration of molecules) is higher than the numerator, and the acid is weak.

What is pKₐ?

The term pK

_{a}is nothing but the negative logarithm of the acid dissociation constant (K_{a}), taken to the base 10._{a}is often too large or too small, so the pK

_{a}is a better alternative for chemical calculations. However, it is commonly seen that the term 'acid dissociation constant' is incorrectly used to refer to both, the K

_{a}and pK

_{a}values , when it is only apt for the former.

_{a}to K

_{a}.

pK

_{a}= -log

_{10}(K

_{a})

From the above equation it is clear that the higher the K

_{a}value, the lower pK

_{a}will be. Thus, strong acids have a high K

_{a}and a low pK

_{a}, while weak acids have a low K

_{a}values and a high pK

_{a}.

pKₐ to Kₐ Conversion

Since pK

K

The logarithm of a number x is the exponent that the number 10 should be raised, to obtain x. For example, in case of the number 1000, 10 must have the exponent 3 to obtain 1000, i.e., 10

Antilog (logarithm) = Antilog 3 = 1000 = 10

i.e., the antilogarithm of the exponent (logarithm) gives the value of 10 raised to that exponent, i.e., the value of 10 raised to the logarithm itself. Therefore,

Antilog (-pK

Thus, another formula to convert pK

K

Let's assume that we are given the pK

K

The low pK

_{a}is the negative logarithm of K_{a}, the value of K_{a}can be calculated by simply reversing the above equation. Thus K_{a}is the antilogarithm of the negative of pK_{a}.K

_{a}= antilog (-pK_{a})The logarithm of a number x is the exponent that the number 10 should be raised, to obtain x. For example, in case of the number 1000, 10 must have the exponent 3 to obtain 1000, i.e., 10

^{3}= 1000. Thus, the logarithm of 1000 is 3. On the other hand, if we are given only the logarithmic value, i.e., 3, then, to find the value of the number from which this logarithm was obtained, we have to take the antilogarithm of this logarithmic value.Antilog (logarithm) = Antilog 3 = 1000 = 10

^{3}= 10^{logarithm}i.e., the antilogarithm of the exponent (logarithm) gives the value of 10 raised to that exponent, i.e., the value of 10 raised to the logarithm itself. Therefore,

Antilog (-pK

_{a}) = 10^{(-pKa)}Thus, another formula to convert pK

_{a}into K_{a}is to find the value of 10 raised to the negative pK_{a}value.K

_{a}= 10^{(-pKa)}**Example**Let's assume that we are given the pK

_{a}value of hydrochloric acid, pK_{a}= -7. Let us find its K_{a}value from the above expressions.K

_{a}= antilog (7) = 10^{7}(Since -(-7) = 7)The low pK

_{a}and large K_{a}values indicate that hydrochloric acid is a strong acid, which readily splits into its ions (H^{+}and Cl^{-})._{a}value can be calculated in a single step, if the pK

_{a}value is available. Acids with a K

_{a}value less than 1 are considered weak, while those with values higher than 1 are strong.