[hohfixer]

I'm looking for the derivation of the formula mg/L (or ppm since I write about water treatment) = Lbs/Gal x 120,000.

[Borek]

Please read forum rules.

[hohfixer]

I have read the forum rules and I can't see anything that I have violated. I'm a semi-retired engineer who writes a monthly Q & A column for Water Technology magazine (my only work) and I'm trying to give a water conditioning dealer a little background on this widely used formula.

[Borek]

The general idea is that you have to try by yourself first - or at least show that you have tried.

To be honest with you - it is a HS level dimensional analysis problem. I find it hard to believe that any engineer can have a problem with it. But I can easily imagine a kid that can't do it and looks for help pretending to be an enginner.

[hohfixer]

I am not a chemical engineer. I have always dealt with valves, controls, piping systems, etc.
I have spent some time on this and no matter how I do it I come out with the 120,000 constant to be in the denominator instead of the numerator, when I try to duplicate the derivation. I know that the 120,000 comes from 1,000,000/8.33 lbs per gallon but I can't make it come out on "top". I start with one pound over a million pounds and then convert the 1,000,000 to 120,000 pounds but never get it complete.
By the way, this "kid" is 63 years old and I'm very sorry to dissappoint you with my lack of high knowledge but that's the way it is.

[Borek]

Then it must be one of these irritating errors that you can't see at first, and later you don't understand how you could not spot them at the first glance. Still, it'll be easier if you post your work

1 lbs / 1 gal x (1 gal / 3.785 L x 453.6 g / 1 lbs x 1000 mg / 1 g)

1 lbs / gal x (120,000 mg x gal x L^-1 x lbs^-1) = 120,000 mg/L

part in the parentheses is the conversion factor.

By the way, this "kid" is 63 years old and I'm very sorry to dissappoint you with my lack of high knowledge but that's the way it is.

That's not the thing - I am ready to help everybody. But you will be surprised how often we are asked simple questions by people that have not tried to find out the answer by themselves. People are even ready to ask how much is 5 times 5 without first Googling it

[hohfixer]

Your result is: 1 lbs / gal x (120,000 mg x gal x L-1 x lbs-1) = 120,000 mg/L

If I solve for mg/L in your formula, which is what I want, then I have: mg/L = (1 lbs/gal)/120,000 with the 120,000 in the denominator. The formula normally used is...ppm = lbs/gal x 120,000.
What am I missing here? Your result reads like the common conversion from lbs/gal to mg/L which I also tried to start with but without sucess.
I considered that there was some problem with ppm vs mg/L but when dealing with concentrations in water this should matter.

[Borek]

You don't have to solve for mg/L. In a way it is already solved. Formula for conversion is:

X mg/L = (120,000 mg * gal * L^-1 * lbs^-1) * Y lbs/gal

Equation (as I have put it) was rather an example of making a conversion - 1 lbs/gal gives 120,000 mg/L.