Chemistry
posted by JayJay .
A solution of household bleach contains 5.25% sodium hypochlorite, NaOCl, by mass. Assuming that the density of bleach is the same as water, calculate the volume of household bleach that should be diluted with water to make 500.0 mL of a pH = 10.10 solution.

5.25% NaOCl by mass means 5.25 g NaOCl/100 g soln and if the density is 1.00 g/mL (as is water) then molarity NaOCl solution is (5.25/74.44) mols NaOCl in 0.1L; therefore, M = 0.075/0.1L = estimated 0.71M. For pH = 10.10 is pOH 1410.10 = 3.90 and since pOH = log(OH^) then (OH^) = about 1.3E4 but you need to do that more accurately.
OCl^ hydrolyzes in H2O as
........OCl^ + HOH ==> HOCl + OH^
I........x..............0......0
C...1.3E4...........1.3E4..1.3E4
E....x1.34E4........1.3E4..1.3E4
Kb for OCl = (Kw/Ka for HOCl) = (1.3E4)^2/(x1.3E4). You know Kw and Ka, solve for x = (OCl^) needed. That comes out to approximately 0.05 but you should confirm that. I just did a quickie on the calculator.
Then c1v1 = c2v2
c = concn
v = volume
0.71*v1 = 0.05*500 mL
Solve for v1.