If you have 120. mL of a 0.100 M TES buffer at pH 7.55 and you add 3.00 mL of 1.00 M HCl, what will be the new pH? (The pKa of TES is 7.55.)

The new pH after adding HCl is 7.07

Explanation:

The formula for calculating pH of a buffer is

pH = pKa + log ([Conjugate base]/[Acid])

Before adding HCl,

7.55 = 7.55 + log ([Conjugate base]/[Acid])

⇔ log ([Conjugate base]/[Acid]) = 0

⇔ [Conjugate base] = [Acid] = 1/2 x 0.100 = 0.05 M

⇒ Mole of Conjugate base = Mole of Acid = 0.05 M x 0.12 mL = 0.006 mol

After adding HCl (3.00 mL, 1.00 M)

⇒ Mole of HCl = 0.003 x 1 = 0.003 mol)

New volume solution is 120 m L + 3 mL = 123 mL

HCl is a strong acid, it will convert the conjugate base to acid form, or we can express

Mole of new Conjugate base = 0.006 - 0.003 = 0.003 mol

⇒ Concentration = 0.003/0.123 M

Mole of new Acid form = 0.006 + 0.003 = 0.009 mol

⇒ Concentration = 0.009/0.123 M

Use the formula

pH = pKa + log ([Conjugate base]/[Acid])

= 7.55 + log (0.003 / 0.009) = 7.07