pKa Value

When we refer to acids and bases, two important terms pH and pK_a are usually used. The pK_a value is employed to determine the strength of an acid. The lower the pK_a of a Bronsted acid, the more simply it provides up its proton. Also, the acidic strength is high as well. The more the pK_a of a Bronsted acid, the more tightly the proton is present, and therefore the less simply the proton is given up which means basic strength is low. The pK_a And pK_b values are related to each other; when one increases the other decreases.

What Is pK_a?

pK_a is the negative base -10 log of the acid equilibrium constant (K_a) of a solution.

\[pK_a = -\log \left[ K_a \right]\]

The lower the pK_a value, the stronger the acid, for instance, trifluoroacetic acid, benzoic acid and acetic acid are 0.23, 4.19 and 4.76, respectively. Using the pK_a values, one can see that trifluoroacetic acid could be a stronger acid than benzoic acid and acetic acid.

The reason pK_a is considered is because it describes acid dissociation with small decimal numbers. A similar form of information could also be obtained from K_a values; however, they are usually very low numbers given in scientific notation that are difficult for many individuals to grasp.

Calculation of pK_a Value

When an acid (HA) dissolves in water, it donates a proton, and therefore the product of the reaction consists of \[{{H}_{3}}{{O}^{+}}\] and \[{{A}^{-}}\], which is the conjugate base of the reaction. Looking at the relative skills of HA to donate protons and \[{{A}^{-}}\] to simply accept them, the reaction may also proceed in the other way till eventually an equilibrium is achieved.

Chemists confirm the strength of an acid (K_a) by measuring the concentrations of HA, \[{{H}_{3}}{{O}^{+}}\] and \[{{A}^{-}}\] at equilibrium and dividing the concentrations of the product by the concentration of the initial acid because the concentration of water may be a constant, they leave it out of the equation.

\[K_a=\frac{\left[ {{H}_{3}}{{O}^{+}} \right]\left[ {{A}^{-}} \right]}{\left[ HA \right]}\]

Conversion to pK_a

For example, the K_a value for hydrochloric acid (HCl) ≃ \[{{10}^{7}}\]

And, the K_a value for ascorbic acid (Vitamin C) ≃ \[1.6\times {{10}^{-12}}\]

Working with such numbers is inconvenient, therefore to create things comprehendible, chemists have outlined the pK_a range as

\[pK_a=-\log \left[ K_a \right]\]

According to this definition, the pK_a value for HCl is as follows:

\[pK{{a}_{\left( HCl \right)}}=-\log {{10}^{7}}=-7\]

Whereas the pK_a for ascorbic acid is:

\[pK{{_a}_{\left( ascorbic \ acid \right)}}=-\log 6\times {{10}^{-12}}=11.80\]

As is clear, the smaller the pK_a value, the stronger the acid.

pK_a and pH of Buffer Solution

The pH scale could be a measure of the concentration of H ions in a solution. pK_a and pH are connected. The relationship between pH and pK_a is represented by the Henderson Hasselbalch equation.

If you recognise either pH or pK_a, you can solve it with the help of an approximation known as the Henderson-Hasselbalch equation:

\[pH=pK_a+\log \frac{\left[ conjugate~base \right]}{\left[ weak~acid \right]}\]

\[pH=pK_a+\log \frac{\left[ {{A}^{-}} \right]}{\left[ HA \right]}\]

pH is the total of the pK_a value and the log of the concentration of the conjugate base divided by the concentration of the weak acid.

At half the equivalence point:

\[pH=pK_a\]

Typically this equation is written for the Ka value instead of pKa,

\[pK_a=-\log \left[ K_a \right]\]

List of pK_a Values

Some of the pK_a values of acids are listed in the following table.

Table: List of Few pKa Values

Relation between pK_a and pK_b

pK_a and pK_b are customary terms in chemistry that are obtained from as dissociation constants. pK_a is obtained from acid equilibrium constant, and pK_b is obtained from base equilibrium constant. The “p” in these terms stands for “negative logarithm”. The key distinction between pK_a and pK_b is that pK_a is the negative log of Ka whereas pK_b is the negative log of k_b.

We know that

\[pK_a=-\log \left[ K_a \right]\]

Similarly, \[pK_b=-\log \left[ K_b \right]\]

The relationship between K_a and K_b are given below.

\[K_w=K_a\cdot K_b\]

Then the connection between pK_a and pK_b is given as (at 25oC)

\[pK_a+pK_b=14\]

pK_a and pK_b are generally comparing the strength of acids and bases. pK_a is given for acid dissociations, whereas pK_b is given for dissociation of bases.

Conclusion

There are connected scales in chemistry usually measuring how acidic or basic a solution is and hence the strengths of acids and bases. pK_a, K_a, pK_b, and K_b are commonly used for the calculations that provide insight into acid-base reactions. The distinction between pK_a and pK_b is that pK_a is the negative log of the K_a whereas pK_b is the negative log of K_b. The higher the value of pK_a, the lower the value of pK_b and acidic strength.