In the titration of $10$ ml $0\mathrm{.}1240$M Na$2$CO$3$ solution with $0\mathrm{.}1100$M HCl solution, find the pH values

a$)$ at the beginning

b$)$ with the addition of $8$ml HCl solution

c$)$ at the $1$st equivalence point

d$)$ with the addition of $20$ ml HCl$.$

$($For H$2$CO$3$ Ka$1=0\mathrm{.}000000445$ Ka$2=0\mathrm{.}0000000000469)$