H2 Chemistry 4 - Theories of Acids and Bases: pH of a Weak Acid

Step 1 - State the problem

Calculate the pH of a zero point one zero molar solution of ethanoic acid, given that its acid dissociation constant K a is one point eight times ten to the minus five moles per cubic decimetre.

Step 1 - State the problem

Ethanoic acid is a weak acid, so it only partially dissociates in water.

Step 1 - State the problem

We need to set up an ICE table and use the K a expression.

Step 2 - Set up the ICE table

Let x be the concentration of hydrogen ions at equilibrium.

Step 2 - Set up the ICE table

Initially, ethanoic acid is zero point one zero molar, and both products are zero.

Step 2 - Set up the ICE table

At equilibrium, ethanoic acid is zero point one zero minus x, and both ethanoate ion and hydrogen ion are x.

Step 2 - Set up the ICE table

Since ethanoic acid is weak and K a is small, we can assume x is much less than zero point one zero.

Step 3 - Write and solve the Ka expression

K a equals the concentration of hydrogen ions times the concentration of ethanoate ions, divided by the concentration of ethanoic acid.

Step 3 - Write and solve the Ka expression

With our assumption, this simplifies to x squared over zero point one zero.

Step 3 - Write and solve the Ka expression

Rearranging: x squared equals one point eight times ten to the minus five times zero point one zero, which is one point eight times ten to the minus six.

Step 3 - Write and solve the Ka expression

Taking the square root: x equals one point three four times ten to the minus three.

Step 4 - Check the assumption and calculate pH

Check the assumption: x is one point three four times ten to the minus three, which is one point three four percent of zero point one zero.

Step 4 - Check the assumption and calculate pH

Since this is well under five percent, the assumption is valid.

Step 4 - Check the assumption and calculate pH

Now calculate pH: pH equals minus log of the hydrogen ion concentration.

Step 4 - Check the assumption and calculate pH

pH equals minus log of one point three four times ten to the minus three, which gives two point eight seven.

Step 5 - Summarise and note common pitfalls

The pH of zero point one zero molar ethanoic acid is two point eight seven.

Step 5 - Summarise and note common pitfalls

Note that a strong acid at the same concentration would have a pH of one point zero zero, because it fully dissociates.

Step 5 - Summarise and note common pitfalls

Common mistake: treating a weak acid as fully dissociated and writing pH equals minus log of the initial concentration.

Step 5 - Summarise and note common pitfalls

Always use the K a expression for weak acids, and always check that your approximation is valid.