$($a$)$ Calculate the $pH$ of a buffer system containing $1\mathrm{.}0MC{H}_3\frac{C}{O}OH$ and $1\mathrm{.}0MC{H}_3\frac{C}{O}ONa.$

$($b$)$ What is the $pH$ of the buffer system after the addition of $0\mathrm{.}10$ mole of gaseous $HCl$ to $1\mathrm{.}0L$ of the solution? Assume that the volume of the solution does not change when the $HCl$ is added.