What volume of 0.2 M sodium benzoate solution must be added to 50 mL of 0.1 M benzoic acid to prepare a buffer solution of pH = 4.5 ? [Given: pK _ a of benzoic acid = 4.2 ; 2 = 0.3 ]

Step-by-step solution

The mixture of benzoic acid and sodium benzoate forms an acidic buffer. Using the Henderson-Hasselbalch equation in terms of moles: pH = pK _ a + n_ salt n_ acid Given values: pH = 4.5 pK _ a = 4.2 Moles of acid ( n_ acid ) = M V = 0.1 M 50 mL = 5 mmol Substitute the values into the equation: 4.5 = 4.2 + ( n_ salt 5 ) 0.3 = ( n_ salt 5 ) Since 2 = 0.3 , we have: n_ salt 5 = 2 n_ salt = 10 mmol The required volume of the 0.2 M sodium benzoate solution is: V_ salt = n_ salt M_ salt = 10 mmol 0.2 M = 50 mL Answer: 50