Dosing equation

Do anyone know the equation in picture below?

I set up a dosing system to calculate a new batch but I can't seem to figure out the computation to dose a certain concentration into the existing concentration to reach a concentration set point !

I started converting everything to wt% to vol% then it got late and I'm getting more confused!


Info you may need to help me get there.

Bulk solution is 50% NaOH which is 12.7 pounds per gallon
Water is 8.3

For sake of example let's assume these parameters


Tank targets : 11% NaOH concentration and volume @ 2200 gallons

Current Tank status : 8% NaOH concentration and volume @ 1885

So I'm down 3% on my NaOH and need 315 gallons.

I would like to figure out a formula to know at what concentration mixture the 315 addition should be to reach 11%.

I was getting really close to figuring it out but last track of what I was doing while shuffling through a dozen examples on my notepad.

This is how I would work it out.


NaOH SP in gallons is: 242 Gals
NaOH PV in gallons is: 150.8 Gals

You need to add: 91.2 Gals

Water deficit is: Capacity - Actual : 2200 - 1885 : 315 Gals

(NaOH Required / Water Required ) * 200

* 100 for % of NaOH if at 100% concentration, as yours is 50% times by 200

So in this example you need to add 315 Gals of a 57.9% concentration of NaOH / Water.