# Is there a name for this algorithm to calculate the concentration of a mixture of two solutions containing the same solute?

There is an algorithm called "Mischungskreuz" (German for "x of mixing") that is sometimes taught as a shortcut to figure out the following problem:

You have two solutions that contain a solute at different concentrations $$c_1$$ and $$c_2$$. At what ratio $$V_1/V_2$$ do you have to mix them so that the mixture has the desired concentration $$c_m$$?

For example, let's say you want to make a 22% solution from a 35% and a 15% solution. You write the desired concentration in the center and the available concentrations at the left ends of the "x", and get the ratio of volumes on the right side of the "x" as shown below:

So in this case, mix 7 parts of 35% with 13 parts of 15% solution to get the desired 22%.

My questions are: Is this method taught outside of Germany, and is there a non-German (maybe English?) name for it?

• Cute. I never saw that before.
– MaxW
Commented Mar 23, 2019 at 22:24
• Very interesting! I have not seen it any English textbook so far. I am an analytical chemist. Most English books teach the dilution formula or mass balance as CiVi=CfVf. The German mixing cross (if this translation is better of Mischungskreuz) is a short cut to solve two problems. If you check Wörterbuch der Chemie / Dictionary of Chemistry: Deutsch/Englisch - English, it also calls it the dilution formula. books.google.com/…
– ACR
Commented Mar 23, 2019 at 22:25
• I repostt my comment, originally to the answer below, for maximum visibility: I do have an important comment and I am not sure if I should write it in form of answer. From a physical chemical point of view this rules is simply wrong. A fact that likely explain why isn't teached or widespread. Of course by contingencies, though wrong, it can be useful, for instance for preparing cleaning or conditioning solutions, of for purposes with little or no physical chemical and analytical relevance. This likely explains why it was(is?) familiar to those working in dairy or sugar industries. Commented Mar 25, 2019 at 8:59
• As was already pointed out, you cannot reliably use the Mischungskreuz to calculate mixtures this way, mostly because volume is not necessarily a conserved quantity - think mixing Ethanol and Water; the sum of the mixture is less than its constituent parts, which really messes up the whole calculation and therein lies the crux of the matter. Which is exactly why the Mischungskreuz is taught (at least where i live) utilizing mass & mass fractions, since those are conserved quantities and the math checks out again. Hope this helped. Commented Feb 27 at 11:10
• @CoffeeAddict This is a comment rather than an answer to the original post. Commented Feb 27 at 12:02