#### Ivor Joedy

##### Well-known member

- Apr 14, 2019

**CASE 1 : CDF-1**

Increasing lower concentration with material of higher concentration

**CASE 2 : CDF-2**Increasing concentration with undiluted material

**CASE 3 : CDF-3**

Decreasing higher concentration with material of lower concentration

**CASE 4 : CDF-4**

Decreasing concentration with pure solvent

**CASE 5 : CDF-5**

Decreasing pure material with pure solvent

**CASE 6 : CDF-6**

Mixing several dilutions with different weights and concentrations

**Let us call**

**$D target bottle**

$S source bottle, solvent

D [g] initial weight of material in target bottle

d [%] initial concentration in target bottle

S [g] initial weight of material in source bottle (we are not interested in this)

s [%] concentration in bottle

S’[g] weight of the material to be transfered from bottle $S to bottle $D

r [%] desired final concentration in target bottle $D

k [ ] coefficient of dilutions

$S source bottle, solvent

D [g] initial weight of material in target bottle

d [%] initial concentration in target bottle

S [g] initial weight of material in source bottle (we are not interested in this)

s [%] concentration in bottle

S’[g] weight of the material to be transfered from bottle $S to bottle $D

r [%] desired final concentration in target bottle $D

k [ ] coefficient of dilutions

**Common Dilution Formula**

**S’ = D * { (r - d) / (s - r) }**

or

**S’ = D * k**

where

**k = { (r - d) / (s - r) }**

**Principle**

Suppose we have a 10% dilution of some material in our target bottle and a 50% dilution in our source bottle,

and we want to increase the concentration in the target bottle to 20%

**k = (20 - 10) / (50 - 20) = 1/3 or 0.3333**

**S' = D * 0.3333**

**This means**: Whatever the weight in the target bottle is, in order to increase the concentration to 20%,

we have to add material from the source bottle in a quantity equal to a third of this weight.