Answer the prompts below to demonstrate why $416mg$ of NaCl corrects the $pH$ after dilution.

The pKa of $H_{2}P{O}_4^{-}$is $6\mathrm{.}89$ at $0\mathrm{.}0500M$ and $23C($using Equation $2$ from the lab background$).$ Show how the

Henderson$-$Hasselbalch equation calculates that the concentrations of $H_{2}P{O}_4^{-}$and $HP{O}_4^{2-}$ are $0\mathrm{.}0355M$

and $0\mathrm{.}0145M$ respectively at $pH=6\mathrm{.}50$ and $23C.[8]$

Using Equation $3$ from the lab background, demonstrate that the ionic strength of the buffer in Step $1$ is

$0\mathrm{.}0790M.$ Hint, include the sodium ions from both the buffer salt and the added NaOH. $[6]$

After $10-$fold dilution, the ionic strength is one$-$tenth the original value that you calculated in Step $1.$ Show

work to demonstrate that $416mg$ of NaCl$(FW=58\mathrm{.}44\frac{g}{m}ol)$ is required to restore the ionic strength, and

thus pKa, of the solution to its original value. $[8]$