Question

common methods to prepare a buffer.

Calculate the mass of benzoic acid and sodium benzoate (in grams) needed to prepare 250 mL of a 0.1 M buffer at pH = 4.1. (The buffer concentration is defined as the sum of the conjugate acid concentration plus the conjugate base concentration.) The pKa of benzoic acid is 4.2

Answer 1

let concentration of benzoic acid be x
then, concentration of benzoate = 0.1 - x
use,
pH = pKa + log([benzoate]/[benzoic acid])
4.1 = 4.2 + log{(0.1-x)/x}
log{(0.1-x)/x} = -0.1
(0.1-x)/x = 10^-1
(0.1-x)/x = 0.1
0.1 - x = 0.1x
1.1x = 0.1
x = 0.091 M

molarity = 0.091 M
volume of solution = 250 mL
= 0.250 L
number of mole of acid = (molarity)*(volume of solution)
= (0.091*0.250) mol
= 0.023 mol

molar massof benzoic acid = 122.1 g/mol
mass of benzoic acid = (number of mole)*(molar mass benzoic acid )
= 0.023*122.1
= 2.8 g

Answer : 2.8 g