Question

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 = 10.18 solution.

Answer 1

Knowing the pH you need to calculate the amount of NaOCl, from the reaction of the OCl- in water:

<--- in this reaction you have OH, hence you need to converte the pH into pOH (pOH=14-pH=14-10.18=3.82)

assuming you added X concentratio, you need to analiza the concentrations in the equilibrium, knowing the pOH is 3.82 and the concentration of OH is 10^-3.82 M

initial	X
equilibrium

In the dissociation the acid and the OH have the same concentration

using the mass action equation (Kb=10^-6.47 value from tables)

solving for X:

<- this is the concentration of OCl you need to add

since the molar relation of OCl and Na is 1:1, the concentration of NaOCl is 0.06776M

using the molar weight calculate the grams (74.5g/mol):

since the bleach has 5.25% by mass, it means 5.25g NaOCl/100g bleach

since the density is the same as water (1g/mL), you need 47.38mL of bleach

There are some variation on the pKa value for HClO, depending on the reference used

If you use the value pKa=7.46 instead of the used above (pKa=7.53)

pKb=14-7.46=6.54 Kb=10^-6.54

Doing the same procedure, using this constant the volume is:

56.5mL