The total cation content of natural water is often determined by exchanging the cations for

hydrogen ions on a strong$-$acid ion$-$exchange resin. A $25\mathrm{.}00$ mL sample of a natural water

was diluted to $100\mathrm{.}00$ mL with distilled water, and $2\mathrm{.}06$ g of a cation$-$exchange resin was

added. After stirring, the mixture was filtered and the solid remaining on the filter paper was

washed with three $15\mathrm{.}00$ mL portions of water. The filtrate and washings required $16\mathrm{.}30$ mL

of $0\mathrm{.}0282$ M NaOH to give a bromocresol green end point.

a$)$ Calculate the number of millimoles of cation present in exactly $1\mathrm{.}00$ L of sample $[8$ mks$]$

b$)$ Report the results in terms of milligrams of CaCO$3$ per liter.