Chemistry Notes

7.2.7 Weak Acids and Ka

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The Acid Dissociation Constant ()

Since weak acids only partially dissociate, we cannot just say

We must use an equilibrium constant to calculate the equilibrium concentration of .

For a weak acid :

The expression for the Acid Dissociation Constant is:

Units of

For the use case of this syllabus, it can be said that always has units of .

How relates to acid strength

  • Large value of
    • Equilibrium lies to the right (stronger acid)
  • Small value of
    • Equilibrium lies to the left (weaker acid)

vs

  • Just like , values are often very small and difficult to work with (e.g. ).
  • We convert them using p-notation :

The Inverse Relationship of with acid strength

  • Stronger Weak Acids have Higher and Lower .
  • Weaker Weak Acids have Lower and Higher

Example:

AcidStrength
MethanoicStronger
EthanoicWeaker

Calculating pH of Weak Acids

To calculate pH, we need to find using the expression for the given acid’s (partial) dissociation:

The Two Approximations

We can simplify the expression using two key approximations.

1. Ignore from water

The Approximation

Therefore:

The Explanation:

  • Although pure water produces a tiny amount of (), the weak acid produces significantly more.
  • Therefore, we assume all ions come from the acid.

Since

produces ions in a ratio, if we ignore water, the concentration of must (approximately) equal the concentration of :

Therefore, the numerator

becomes:

2. Dissociation is Negligible

The Approximation

The Explanation:

  • Weak acids dissociate very slightly (often < 1%).
  • Therefore, the amount of acid molecules that break apart is mathematically insignificant compared to the large amount that remain intact.

Since is tiny,

Therefore, instead of finding out the concentration of at equilibrium to use in the denominator of the expression, you can just use the concentration of you started with (e.g. if the bottle you got the acid from said , you use that as in the expression).

The Simplified Formula

Substituting these approximations into the expression:

Rearranging to solve for :

Example: Calculating pH of ethanoic acid

Calculate the pH of ethanoic acid. ()

  1. Calculate
  2. Calculate pH

Limitations of the Approximations

The formula

works most of the time. However, the assumption that dissociation is negligible fails if:

  1. The acid is stronger than usual ()
  2. The solution is extremely dilute

Graph View

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