Asolution 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.

The hypochlorite ion, OCl-, acts as a base in water, removing a proton from water and forming the weak acid HOCl, according to:
OCl−1+H2O→HOCl+OH−1
Use the required pH to find the needed [OH] concentration.
Use the volume and concentration to get the needed moles of [OH] Use the molar ratio between OH and NaOCl to get the needed moles of NaOCl
Use the molar mass of NaOCl to get the needed mass of NaOCl.
But 100g of "bleach" won't contain 100g of NaOCl,
so you need to find what volume of bleach, at 5.25% my mass, contains that needed mass of NaOCl.