Formula for calculating amount needed for target concentration

[StringJunky]

Is there a general formula for determining the amount of solution A, of concentration x%, required to mix with solution B, of concentration y%, to make a solution C that has a final concentration of z%.? A is the stronger stock solution and B needs raising.

As an example, I have a 10% stock solution (Solution A) and I want to raise 150ml of 0.5% solution ( Solution B) to 2% (Solution C).

[DrP]

A simple substitution of that 10% solution will give you dilution for a new constitution to achieve your resolution of a 2% solution which seems to be the target of your convolution.

 

Can you just simply dilute some of the 10% stock straight down to 2%? It will be easier to work out and quite simple. Otherwise - break it into first principles and do the algebra required to change the 0.5% into a 2% solution. I normally write it out in pencil on a piece of paper listing what I have, what I want and what I need to get there.

PS - I say that diluting some of the 10 % solution might be more accurate as you will be dealing with whole round numbers without having to round off any decimal places. The dilution from 10 to 2 % will be easy with no recurring decimal places to worry about - depends what you need it for I suppose.

[StringJunky]

A simple substitution of that 10% solution will give you dilution for a new constitution to achieve your resolution of a 2% solution which seems to be the target of your convolution.

 

Can you just simply dilute some of the 10% stock straight down to 2%? It will be easier to work out and quite simple. Otherwise - break it into first principles and do the algebra required to change the 0.5% into a 2% solution. I normally write it out in pencil on a piece of paper listing what I have, what I want and what I need to get there.

PS - I say that diluting some of the 10 % solution might be more accurate as you will be dealing with whole round numbers without having to round off any decimal places. The dilution from 10 to 2 % will be easy with no recurring decimal places to worry about - depends what you need it for I suppose.

That was just an example. I'm more interested in the principle. The aim is to use the stock to make corrections to a made up flavour recipe gone wrong and correcting one of the components.

Edited June 7, 2017 by StringJunky

[KipIngram]

This is pretty straightforward algebra. If you have a solution of A ml with concentration "a" g/ml and another of B ml of concentration "b" g/ml, then mixing them gives you a total volume of A+B and a total solute mass of Aa+Bb, so your new concentration is (Aa+Bb)/(A+B). If you start with the first and want to add the second to get a final concentration of "c" g/ml, then

 

c = (Aa+Bb)/(A+B)

 

Ac + Bc = Aa + Bb

 

Ac - Aa = Bb - Bc

 

You have both B and b to play with - if you specify B then

 

b = (Ac - Aa - Bc) / B

 

whereas if you specify b then

 

B = (Ac - Aa) / (b - c)

[StringJunky]

This is pretty straightforward algebra. If you have a solution of A ml with concentration "a" g/ml and another of B ml of concentration "b" g/ml, then mixing them gives you a total volume of A+B and a total solute mass of Aa+Bb, so your new concentration is (Aa+Bb)/(A+B). If you start with the first and want to add the second to get a final concentration of "c" g/ml, then

 

c = (Aa+Bb)/(A+B)

 

Ac + Bc = Aa + Bb

 

Ac - Aa = Bb - Bc

 

You have both B and b to play with - if you specify B then

 

b = (Ac - Aa - Bc) / B

 

whereas if you specify b then

 

B = (Ac - Aa) / (b - c)

Thanks Kip.

[KipIngram]

I guess we could go one better and say we wanted to specify both c and C - then you have

 

C = A + B

 

c = (Aa + Bb) / (A + B)

 

or

 

B = C-A

 

b = (cA + cB - Aa)/B

 

So starting with A of "a" and wanting C of "c", that tells you to add B of "b".

[studiot]

Yes, I'd add +1 to Kip as well.

 

But I'd also add that Kip's agebra works mass concentrations, useful now that we know we are talking about a food recipe.

You did post this in Inorganic Chemistry where a Chemist might be forgiven for thinking molar concentrations, and why not organic chemistry for food?