How do you use the henderson-hasselbalch equation to calculate changes in pH?

The added acid will protonate the acetate, thus lowering its concentration. The acetic acid concentration will rise.

We needed to determine the moles of Ac- and HAc present before adding the HCl.

Both are 0.1 mole. You may verify this.

we added (0.1 L) (0.1 mol/L) = 0.01 mole of HCl.

Therefore the HAc goes from 0.1 mol to 0.11 mole and the Ac- goes 0.1 mol to 0.09 mol.

Notice that the total volume rises from 1 L to 1.1 liter. This will create new molarities, but I will ignore the molarity calculation. This is because the ratio portion of the H-H will work just fine with the mole amounts.

pH = 4.76 + log (0.09/0.11) gives the answer.