Using the equations $($discussed above$)$ showing the relationship between $[$acid$],[$conjugate base$],$ and $[$buffer concentration$],$ mathematically show the negligible change in $pH$ even when $2L$ of $10MHCl$ is added to $100mL$ of $50mM$ phosphate buffer at $pH6\mathrm{.}9.$ To address this problem, the following steps will be needed: $($i$)$ You will have to calculate the $pH$ of the buffer after adding the $2L$ of $10MHCl($ii$)$ To do this, calculate the new concentration of $[$acid$]$ and $[$conjugate base$]$ after the addition of $2Lof10MHCl,$ and $($iii$)$ To appreciate the effect of buffers, show the $pH$ change in $100mL$ of water after adding $2L$ of $10MHCl$ that does not contain the phosphate buffer ions. $($Show all calculation steps$)$ Points $15($H$-$H equation: $1+$ calculation of $[$acid$]$: $4+$ calculation of $[$conjugate base$]$: $4+$ calculation of new $pH$:$3+$ calculation of $pH$ of water upon addition of $HCl$:$3)$