A-level Chemistry/OCR (Salters)/Weak acids

Calculating the pH of a weak acid solutionEdit

The pH of a weak acid solution can be calculated approximately using the following formula:

 

DerivationEdit

For any equilibrium

 

the equilibrium constant, K, is defined as

 

Therefore, for the dissociation equilibrium of any acid

 

the acid dissociation constant, Ka, is defined as

 

Two assumptions are required:

1 The concentrations of H+(aq) and A(aq) are equal, or in symbols:

 
The reason this is an approximation is that a very slightly higher concentration of H+(aq) exists in reality, due to the autodissociation of water, H2O(l) H+(aq) + A(aq). We neglect this effect since water produces a far lower concentration of H+(aq) than most weak acids. If you were studying an exceptionally weak acid (you won't at A-level), this assumption might begin to cause big problems.

2 The amount of HA at equilibrium is the same as the amount originally added to the solution.

 
This cannot be quite true, otherwise HA wouldn't be an acid. It is, however, a close numerical approximation to experimental observations of the concentration of HA in most cases.

The effect of assumption 1 is that

 

becomes

 

The effect of assumption 2 is that

 

becomes

 

which can be rearranged to give

 

and therefore

 

By definition,

 

so