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3.4.3 Acids and Bases - Weak acids and bases

Specification

Students should:
  • understand Ka for weak acids
  • know that weak acids and weak bases dissociate only slightly in aqueous solution
  • be able to construct an expression, with units, for the dissociation constant Ka for a weak acid
  • know that pKa = -log10 Ka
  • be able to perform calculations relating the pH of a weak acid to the dissociation constant, Ka, and the concentration pH curves, titrations and indicators
  • understand the typical shape of pH curves for acid-base titrations in all combinations of weak and strong monoprotic acids and bases
  • be able to use pH curves to select an appropriate indicator
  • be able to perform calculations for the titrations of monoprotic and diprotic acids with sodium hydroxide, based on experimental results

The acid dissociation constant

Acids are substances which dissociate in aqueous solution giving solvated hydrogen ions.

HA + H2O H+(aq) + A-(aq)

This is an equilibrium and can be expressed by the equilibrium law. However, as the concentration of water is effectively constant and in huge excess it makes sense to define a dissociation constant without the water. This is called the acid dissociation constant, ka.

Using the dissociation example above:  

The value of ka, i.e. degree to which this dissociation happens, defines the strength of the acid. Strong acids have high ka values and weak acids have low ka values.

In reality, strong acids dissociate 100% into ions and it makes no sense to use ka values to describe their strength.

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Strong and weak acids

Although there is no hard and fast distinction dividing line between strong and weak acids, it is generally assumed that strong acids dissociate 100% in aqueous solution and weak acids don't.

Strong acids ka
sulfuric acid > 1
hydrochloric acid > 1
nitric acid > 1
Weak acids  
methanoic acid 1.77 x 10-4
ethanoic acid 1.78 x 10-5
carbonic acid 3.98 x 10-7

As can be seen in the table above, the values of ka are usually very small for weak acids and for this reason another scale is used in which the ka value is converted into the negative log 10 value. This is called the pKa.

Weak acids ka pKa
methanoic acid 1.77 x 10-4 3.75
ethanoic acid 1.78 x 10-5 4.75
carbonic acid 3.98 x 10-7 6.40

The lower the pka value the stronger the acid.

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pH of strong acids

This requires calculation of [H+(aq)], which is a relatively straightforward matter:

Example: Calculate the [H+(aq)] of 0.25 M sulfuric acid

As sulfuric acid dissociates 100% according to the equation

H2SO4 2H+ + SO42-

Then 0.2 M sulfuric acid gives 0.25 x 2 M hydrogen ions solution = 0.5M

The pH of this solution is:

pH = - log 0.5 = 0.3

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pH of weak acids

If we are dealing with a weak acid (or base) then the ka (or pka) of the acid must be known:

Example: Calculate the [H+(aq)] of 0.2 M ethanoic acid (Ka = 1.78 x 10-5)

As ethanoic acid is a weak acid it only partially dissociates according to the equation:

CH3COOH CH3COO- + H+

Applying the equilibrium law:

Ka =
[H+][CH3COO-]
[CH3COOH]

We can assume that as the acid only slightly dissociates then the concentration of the acid at equilibrium is the same (to a close approximation) as the concentration of the original acid (in this case = 0,2 M), Therefore:

1.78 x 10-5 =
[H+][CH3COO-]
[0.2]

And as the hydrogen ion concentration equals the ethanoate ion concentration then:

0.2 x 1.78 x 10-5 = [H+]2

[H+] = √ 3.56 x 10-6

[H+] =1.89 x 10-3

The pH of this solution is:

pH = -log 1.89 x 10-3 = 2.7

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Bases and basicity

In these cases the base removes an ion of hydrogen from the water molecule. The base is hydrolysing (breaking apart) the water to produce hydroxide ions. As the base gains a hydrogen ion, it itself will produce a species with a positive charge (positive ion)

NH3 + H2O NH4+ + OH-

Once again the water is in vast excess and a new constant, kb, is defined as:

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Derivation of Ka x Kb = Kw

For weak acid dissociation of ethanoic acid the equation:

CH3COOH CH3COO- + H+

CH3COOH is the acid and CH3COO- is its conjugate base.

Ka =
[H+][CH3COO-]
[CH3COOH]

And for the conjugate base reaction with water:

CH3COO- + H2O CH3COOH + OH-

Kb =
[OH-][CH3COOH]
[CH3COO-]

Multiplying Ka and Kb gives:

Ka x Kb =
[H+][CH3COO-]
x
[OH-][CH3COOH]
[CH3COOH]
[CH3COO-]

Cancelling out terms from top and bottom gives:

Ka x Kb =
[H+]
x
[OH-]

And as: Kw = [H+][OH-]

Then:

Ka x Kb = Kw

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Acid - base titrations

A titration is where small quantities of one component is added a little at a time to a solution of the other component in the presence of an indicator until the indicator registers the neutral point. Titratinos are used to determine the concentration of solutions. If the stoichiometry of the reaction is known then using a solution of known concentration allows determination of a second solution.

The evolution of pH against volume of component added in an acid-base titration is known as a titration curve.

A graphical plot gives distinctive curves depending on the strength of the acid and base.

Titration curves

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