The pK Scale

Introduction

In our discussion of conductance, we introduced the term acidity constant, K_a, as a measure of the concentration of hydronium ions produced by the dissociation of a compound when it was dissolved in water. In the case of acetic acid, the acidity constant is given by the expression

Mathematical manipulation yields an alternative form of this equation:

The important point about this equation is the relationship between pK_a and the more familiar pH; pH is a measure of the acidity of a solution, i.e. the concentration of hydronium ions, while pK_a is a measure of the inherent acidity of a compound, i.e. the tendency of a compound to transfer a proton to a base. These parameters vary in the same way: the lower the pH, the higher the hydronium ion concentration; the lower the pK_a the more acidic the compound. We will use the pK_a scale to gain insight into the variables that determine the acidity of a compound as well as to develop a system for predicting approximate equilibrium constants for a variety of reactions.

Acid-Base Relationships

Consider the generalized representation of an acid-base reaction shown in Equation 1.

In this reaction, an acid, H-A₁, transfers a proton to a base, ^-:A₂, forming a new acid, H-A₂ and a new base, ^-:A₁. The species ^-:A₁ is called the conjugate base of H-A₁; H-A₁ and ^-:A₁ constitute a conjugate acid-base pair. The same terms apply to H-A₂ and ^-:A₂.

Exercise 2 Assume you mixed 100 molecules of H-A₁ with 100 ^-:A₂ ions. If the value of K_eq were 1, at equilibrium the mixture would contain molecules of H-A₁ ^-:A₂ ions molecules of H-A₂ and ^-:A₁ ions.

Exercise 3 Which is the stronger acid, H-A₁ or H-A₂? H-A₁ H-A₂ Neither, they have the same strength.

Exercise 4 If the value of K_eq were 10 rather than 1, which compound would be the stronger acid? H-A₁ H-A₂

Exercise 5 If the value of K_eq were 0.1 rather than 1, which compound would be the stronger acid? H-A₁ H-A₂

By the same token, if an acid is very reactive, its conjugate base is very non-reactive, i.e. very stable.

In any acid-base equilibrium, the equilibrium will favor the less reactive, more stable compounds. In other words, the equilibrium constant will be greater than 1 whenever the products of the acid-base reaction are more stable than the reactants. In other words, there will always be more of the weaker acid present in the mixture at equilibrium. This means that if the pK_a of H-A₂ is greater than that of H-A₁, the equilibrium constant for Equation 1 will be greater than 1.

Table 1 lists approximate pK_a values of a representative group of acids. All the values have been rounded to the nearest whole number. The proton that is transferred is shown in red.

Table 1

pK_a Values of Selected "Acids"

Compound	Structure	pKa	Conjugate Base
methane		50
ethene		44
ammonia		38
acetone		19
water		16
methanol		16
phenol		10
acetylacetone		9
acetic acid		5
hydrogen fluoride		3
hydronium ion		-2
hydrogen chloride		-7
hydrogen bromide		-9
hydrogen iodide		-10

Exercise 7 For each of the following acid-base reactions, use the pK_a values given in Table 1 to determine whether the value of K_eq will be greater than, less than, or equal to 1.

	greater	less	equal
	greater	less	equal
	greater	less	equal
	greater	less	equal

The pK_a value of methanol is 16 while that of ammonia is 38. Ammonia is a much weaker acid than methanol. The equilibrium constant for Equation 2, therefore, must be greater than 1. Since the difference between the pK_a values of methanol and ammonia is 38-16=22, the value of K_eq for Equation 2 is approximately 10²². An analysis of this approach is available via the link below.

a. K_eq =

b. K_eq =

pK_a Calculations

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