A buffer with a pH of 4.13 contains 0.29 M of sodium benzoate and 0.34 M of benzoic acid. What is the concentration of [H3O ] in the solution after the addition of 0.054 mol HCl to a final volume of 1.5 L

Explanation:

Formula for pH of a buffer solution

pH = pKa + log ( moles of sodium benzoate / moles  of benzoic acid)

pKa of benzoic acid = 4.2

Volume of solution is 1.5 L .

moles of sodium benzoate = .29 x 1.5 = .435 moles

moles of benzoic acid  = 1.5 x .34 = .51 moles

Addition of HCl will reduce concentration of salt and increase concentration of acid

moles of sodium benzoate after addition of HCl =  .435 - .054 = .381  moles

moles of benzoic acid  =  .51 + .054  = .564 moles

resultant pH = 4.2 + log ( .381 / .564 )

= 4.2 + log .6755

= 4.029

concentration of H⁺ or H₃O⁺ =

= 9.35 X 10⁻⁵ M .

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