Question

The final volume of buffer solution must be 100.00 mL and the final concentration of the weak acid must be 0.100 M. Based on this information, what mass of solid conjugate base should the student weigh out to make the buffer solution with a pH of 1.00

Answer 1

Answer:

0.387 g

Explanation:

pH of the buffer = 1

V = Volume of solution = 100 mL

[HA] = Molarity of HA = 0.1 M

$K_a$ = Acid dissociation constant = $1.2\times 10^{-2}$

(assuming base as $Na_2SO_410H_2O$)

Molar mass of base = 322.2 g/mol

pKa is given by

$pK_a=-\log K_a\\\Rightarrow pKa=-\log(1.2\times 10^{-2})\\\Rightarrow pK_a=1.92$

From the Henderson-Hasselbalch equation we get

$pH=pK_a+\log\dfrac{[A^-]}{[HA]}\\\Rightarrow pH-pK_a=\log\dfrac{[A^-]}{[HA]}\\\Rightarrow 10^{pH-pK_a}=\dfrac{[A^-]}{[HA]}\\\Rightarrow [A^-]=10^{pH-pK_a}[HA]\\\Rightarrow [A^-]=10^{1-1.92}\times0.1\\\Rightarrow [A^-]=0.01202\ \text{M}$

Moles of base

$0.01202\times100\times\dfrac{1}{10^3}=0.001202\ \text{moles}$

Mass of base is given by

$0.001202\times 322.2=0.387\ \text{g}$

The required mass of the base is 0.387 g.