The following solutions have been prepared:

Solution $1$: $H_{2}O$ plus sufficient $HCl$ and$/$or NaOH to attain $pH8\mathrm{.}0.$

Solution $2$: $H_{2}O$ plus ${10}^{-3}$TOTOCl plus sufficient $HCl$ and$/$or NaOH to attain $pH$

$8\mathrm{.}0.$

Solution $3$: $H_{2}O$ plus ${10}^{-2}$ TOTOCl plus sufficient $HCl$ and$/$or NaOH to attain $pH$

$8\mathrm{.}0.$

$($a$)$ In Solutions $2$ and $3,$ one$-$half of the TOTOCl was added as HOCl and one$-$half as

NaOCl. Find the amount of $HCl$ or NaOH needed to adjust the $pH$ of each solution to

$8\mathrm{.}0.$

$($b$)$ Compute and compare the $pH$ when ${10}^{-3}$mol of $HCl$ is added to $1L$ of each of the

solutions.