you extract 10 g of benzoic acid from an ether solution with aqueous NaHCO3

Question

what is the min amount of concentrated HCl (37% by w/v%) that would be needed to convert the sodium benzoat back to free energy? (answer: 8.2 mL)
I know that the 37% is basically 37g/ 100ml but how would that help me?

How many extractions do you need in order to extract at least 95% of the benzoic acid with 15mL of methylene chloride (solvent 2) that are intially presented in 45mL of HCl (solvent 1)? You may assume that the partition coefficient to be 3.5 for the benzoic acid.(answer is 4)
I did something wrong!
10=9.5(45ml/[3.5*15 + 45])^n
solving for n and I don't get 4

Thanks for the help!

Answer 1

I have
f_n = [1+ K_{d*(Vo/Va)]^-n.
where fn = fraction remaining in the water layer. For 95% extraction, that would be 5/100 = 0.05 remaining.
0.05 = 1/[1+3.5(15/45)]ⁿ
I solve for n and I get 3.87 which would be 4 extractions.}

Answer 2

That character that didn't print clearly at the end of the formula is -n for the first one, and n for the second one.
0.05 = 1/[1+3.5(15/45)]^n
0.05 = 1/(2.1667)^n
(2.1667)^n = 1/0.05
etc