A student needs to prepare an acidic buffer of pH = 5.0 using 0.1 M CH ₃ COOH ( p K_a = 4.7 ) and 0.1 M NaOH . What is the required volume ratio of NaOH to CH ₃ COOH to achieve this target pH? (Given 2 = 0.3 )

Step-by-step solution

Using the Henderson-Hasselbalch equation: pH = p K_a + ( [ Salt ] [ Acid ] ) 5.0 = 4.7 + ( [ Salt ] [ Acid ] ) ( [ Salt ] [ Acid ] ) = 0.3 Since 2 = 0.3 , we have [ Salt ] [ Acid ] = 2 Let V_b be the volume of NaOH and V_a be the volume of CH ₃ COOH . Millimoles of NaOH = 0.1 V_b Millimoles of CH ₃ COOH = 0.1 V_a Upon mixing, the strong base completely reacts with the weak acid: Millimoles of salt formed = 0.1 V_b Millimoles of acid remaining = 0.1 V_a - 0.1 V_b Substituting into the ratio: 0.1 V_b 0.1 V_a - 0.1 V_