Determine the pH

Question

What is the pH of a 0.16 M solution of Benzoic acid pKa = 4.202

Answer 1

First, we need to write the chemical equation. We can abbreviate benzoic giving HA > H⁺ + A^-

Next, make an ICE chart with the initial concentrations of [HA] = 0.16M and [H⁺] = [A^-] = 0. Assign a variable of x to the change in concentration for all three. This makes the equilibrium concentrations 0.16-x, x, and x respectively.

Now, write an equilibrium expression, Ka = [H⁺][A^-]/[HA]. From the pKa, Ka = 6.28E-5 = x²/(0.16-x). We'll assume that the x is small enough to ignore compared to the 0.16 (we'll confirm in a second), so it becomes 6.28E-5=x²/0.16. From that x (which is equilibrium [H⁺]), we can calculate pH = -log[H⁺].

Go ahead and check that x is less than 5% of the 0.16 to make sure our assumption above was acceptable. (I got 2%. So, we're good.)

Finally, watch out for the pH sig fig rule - the number of SFs in the concentration is the number of decimal places in the pH.