Lecture 37 Summary

There are about four general cases (depending on how you count them): (1) Strong acid / strong base; (2) Weak acid/ weak base; (3) Buffer; and (4) Intermediate forms of polyprotic acids. Case (4) is covered in Ch.11 of Harris, and we'll get to it in a few lectures. With the tools to calculate pH in each of these cases, it will be possible to calculate an entire theoretical titration curve.

Everything you need to know about acid-base chemistry, continued. Definition and properties of a buffer. Weak acid and weak base equilibria. pH calculations. Fraction of dissociation.

As we begin a thorough study of acid-base chemistry, we will take as our starting point the Brønsted-Lowry defintion of an acid and a base, which simply states that an acid is a H⁺ (sometimes we say "proton" for 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.

For a review of basic concepts of acid-base chemistry, see Introduction to acids and bases and the Brønsted-Lowry defintion webpages.

Strong acid and strong base calculations

A typical problem is to calculate the pH of a solution of a strong acid or a strong base of a given (formal) concentration. This type of problem (see the example on p.161 of Harris, or the first of the example problems for today's lecture) is relatively simple and straightforward, since we can assume that any compound that is a strong acid or strong base in water is completely dissociated.

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

pH, pOH, and other logarithmic functions

Of course, we are probably already familiar with pH, but here's a quickie review. The pH is a logarithmic function of the concentration in water of the hydronium ion (H₃O⁺ - a reasonable representation of the actual species present in excess in acidic aqueous solutions - it is commonly abbreviated as H⁺(aq), or simply H⁺),

pH  =  – log [H⁺].

We can define similarly pOH as

pOH  =  – log [ OH ^– ].

Autoionization of water

The so-called autoionization of water refers to the water molecule's very slight, but measureable, tendency to break apart to form ions:

H₂O   →   H⁺  +  OH ^–

We can quantify water's autodissociation 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.

Using the above value for K_w, and applying the definitions of pH and pOH, as well as the properties of logarithms, it can be easily shown that

pK_w  =  14.00  =  pH  +  pOH    (at 25°C).

Fundamental definitions and relations in acid-base chemistry

"Autoprotolysis" of water.

H₂O  +  H₂O   =   H₃O⁺  +  OH ^–      (abbrev. as   H₂O   →   H⁺  +  OH ^– )

The equilibrium constant for (called K_w ) is defined here as

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

Definition of pH

The pH is a logarithmic function of the hydronium ion concentration (abbreviated as H⁺(aq). )

pH  =  – log [H⁺]           pOH  =  – log [ OH ^– ]

Because (at 25 °C) K_w = 1.0 x 10^–14 :      pH  +  pOH  =  14.00

Base hydrolysis equation:

base +  H₂O  →  base-H⁺  +  OH^–.

Basicity constant, K_b. The equilibrium constant for the base hydrolysis equation, K_b, known as the base hydrolysis constant, or simply "base constant".

K_b  =  [base-H⁺] [OH^–] / [base]

pK_a and acid strength

In general, pK  =  – log K by definition. We commonly use pK_a as an index of acid strength.

pK_a =  – log K_a

The lower the pK_a, the stronger the acid. Hydronium ion has a pK_a of −1.7. Water as an acid has a pK_a of 15.7.

Quick reference tables: [ Strong and weak acids ] [ Strong and weak bases ] [ Table of acid strengths ] .