Lecture 5 Summary

In this lecture, we begin a thorough study of acid-base chemistry. We will take as our starting point the Brønsted-Lowry definition of an acid and a base, which simply states that an acid is a proton (H⁺) donor, and a base is a proton acceptor. The Brønsted-Lowry definition is quite general, and we find it convenient to consider a general Brønsted-Lowry acid, HA, and its corresponding acid dissociation equation:

HA  =  H⁺  +  A^–

Here, HA is the acid, and A^– is the conjugate base of HA. Brønsted-Lowry acids and bases always occur in conjugate pairs, and one of the merits of the acid dissociation equation is that it helps make this fact clear. As a specific example, water can act as an acid when it loses a proton to form hydroxide ion, the conjugate base of water:

H₂O  =  H⁺  +  OH ^– .

It is important for us to realize at the outset that water and some other substances can act as either acids or bases. Such substances are termed amphiprotic. If water is a base, then its conjugate acid must be the result of water accepting a proton. This species, H₃O⁺, is called hydronium ion. The acid dissociation equation for hydronium ion is:

H₃O⁺  =  H⁺  +  H₂O.

One point that is often confusing for students learning acid-base chemistry is that "H⁺" is often used as a shorthand for hydronium ion, or any species representing a proton transferred to water. What we really mean in that case is H⁺(aq), and we should take special care to keep a distinction in mind between H⁺(aq) and H⁺ as written in the acid dissociation equation for any Brønsted acid. In an acid dissociation equation, H⁺ is meant to represent a proton being transferred to another species acting as a base, and thus the equation only represents half of a complete Brønsted-Lowry acid-base reaction. For example, the formation of hydrochloric acid in water is the result of the combination of two acid dissociation equations:

HCl  =  H⁺  +  Cl ^– .

H₃O⁺  =  H⁺  +  H₂O.

The way to combine these is to reverse one of the half-reactions and add the two equations together so that there is an acid and a base on each side of the equation, and the H⁺'s cancel out. The summed equation is thus a proton transfer reaction, which is another way of saying "Brønsted-Lowry acid-base reaction". But which acid dissociation equation should we flip? Well, it really doesn't matter - either way we will get a valid chemical equation from the sum. But if we want to write the summed equation so that the products are favored at equilibrium, we should flip the acid dissociation equation for the weaker acid. We will learn how to quantify acid strength in short order, but for now let's utilize the fact that HCl is a stronger acid than hydronium ion, so let's flip the bottom equation and then sum the equations:

HCl  =  H⁺  +  Cl ^– .

H⁺  +  H₂O  =  H₃O⁺.

sum:  HCl  +  H₂O   =   H₃O⁺  +  Cl ^–.

We have written a proton-transfer (or acid-base) reaction in a form that favors the products at equilibrium. It is worth noting and remembering that the products favored at equilibrium in an acid-base reaction are invariably the weaker acid and the weaker base.

Definition of K_a, the acid dissociation constant

For the general acid dissociation equation,

HA  =  H⁺  +  A^–

we define K_a, the acid dissociation constant, by forming the expression

K_a  =  [H⁺][A^– ] / [HA].

Note how we apply the normal rules for writing an equilibrium constant - concentrations of products in the numerator, concentrations of reactants in the denominator - to the acid dissociation equation in defining K_a. We will use K_a as a quantitative measure of acid strength.

Autoionization (or "autoprotolysis") of water

What if we put together the two acid dissociation equations for water as an acid and hydronium ion?

H₃O⁺  =  H⁺  +  H₂O.

H₂O  =  H⁺  +  OH ^– .

Following the rules above, we would write

H₃O⁺  =   H⁺  +  H₂O

H⁺  +  OH ^–   =   H₂O

sum:  H₃O⁺  +  OH ^–  =  H₂O  +  H₂O.

You may recognize the summed equation as the net ionic equation for the neutralization reaction between a strong acid and a strong base. The reverse of this reaction - written with the products extremely unfavorable at equilibrium - is the so-called autoionization of water. Harris uses the term "autoprotolysis" (see p.154).

H₂O  +  H₂O   =   H₃O⁺  +  OH ^–.

We can quantify water's small tendency to autodissociate by defining a special type of equilibrium constant called K_w and assigning an experimentally determined value to it.

K_w = [ H⁺ ][ OH ^– ] = 1.0 x 10^–14   (at 25°C).

Note that this is the equilibrium constant expression that we would write for the chemical equation representing the autodissociation reaction of water, considering the concentration of water as a constant. The very small value for K_w reflects the very weak propensity of water to autodissociate.

pH, pOH, and other logarithmic functions

One of our learning goals is to know the definition of pH and become very familiar with its use. The pH is a logarithmic function of the hydronium ion concentration (abbreviated here as H⁺),

pH  =  – log [H⁺].

Note the minus sign in the definition creates an inverse relationship between [H⁺] and pH. A very high [H⁺] means pH is low, and vice-versa. But pH varies much less than [H⁺] in magnitude. This is characteristic of logarithmic functions, and make them useful in cases where quantities vary over many orders of magnitude. Another example of such a quantity is K, the equilibrium constant for a reaction. We will want to be able to use pK values, where

pK  =  – log K

to quantify the strength of acids on the same scale as the pH scale.

In the range of hydronium ion concentrations we will typically encounter, the pH ranges between 0 and 14. As we may well know already, a pH of 7 - that is, [H⁺] = 1.0 x 10^–7 M - is considered neutral, and pH less than 7 is considered acidic, while pH > 7 is basic. As a measure of basicity, and a counterpart to pH, we introduce pOH, defined as

pOH  =  – log [ OH ^– ].

Another one of our goals is to know the simple relationship between pH and pOH in aqueous solutions of acidic and basic compounds

pH  +  pOH  =  14

and its basis in the definition and value of the ionization constant K_w.