A buffer must both maintain a pH within of the of weak acid and neutralize of added

CHEMISTRY · Numerical · A Level · Chemistry · Acids and bases · Acids and bases

Problem

A buffer must both maintain a pH within

\pm0.10

of the

\mathrm{p}K_a

of weak acid

\text{HA}

and neutralize

0.0400\,\text{mol}

of added

\text{NaOH}

. Two stock solutions are available:

Stock solution	Cost
$0.20\,\text{M}\ \text{HA}$	$0.04$ dollars per mmol of $\text{HA}$
$0.20\,\text{M}\ \text{NaA}$	$0.06$ dollars per mmol of $\text{A}^-$

The buffer has a total volume of exactly

500\,\text{mL}

, and the

\text{HA}:\text{A}^-

mole ratio must lie between

0.95:1

and

1:0.95

. Calculate the minimum total reagent cost.