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

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4

2

$begingroup$

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%.

Source: https://de.wikipedia.org/wiki/Mischungskreuz

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

solutions analytical-chemistry concentration terminology

share|improve this question

edited 10 mins ago

andselisk

18.3k656121

asked 2 hours ago

Karsten TheisKarsten Theis

3,266538

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Cute. I never saw that before.
  $endgroup$
  – MaxW
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  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/…
  $endgroup$
  – M. Farooq
  1 hour ago
  

  
  
  
  

add a comment | 

4

2

$begingroup$

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%.

Source: https://de.wikipedia.org/wiki/Mischungskreuz

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

solutions analytical-chemistry concentration terminology

share|improve this question

edited 10 mins ago

andselisk

18.3k656121

asked 2 hours ago

Karsten TheisKarsten Theis

3,266538

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Cute. I never saw that before.
  $endgroup$
  – MaxW
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  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/…
  $endgroup$
  – M. Farooq
  1 hour ago
  

  
  
  
  

add a comment | 

$begingroup$

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%.

Source: https://de.wikipedia.org/wiki/Mischungskreuz

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

solutions analytical-chemistry concentration terminology

share|improve this question

edited 10 mins ago

andselisk

18.3k656121

asked 2 hours ago

Karsten TheisKarsten Theis

3,266538

$endgroup$

share|improve this question

edited 10 mins ago

andselisk

18.3k656121

asked 2 hours ago

Karsten TheisKarsten Theis

3,266538

share|improve this question

edited 10 mins ago

andselisk

18.3k656121

asked 2 hours ago

Karsten TheisKarsten Theis

3,266538

edited 10 mins ago

andselisk

18.3k656121

edited 10 mins ago

andselisk

18.3k656121

asked 2 hours ago

Karsten TheisKarsten Theis

3,266538

asked 2 hours ago

Karsten TheisKarsten Theis

3,266538

1 Answer
1

active

oldest

votes

3

$begingroup$

This is a so-called Pearson's square or Box method of balancing ratios, and not only chemical ones.

Widely popularized in Soviet books for analytical chemistry at least since 1940s (probably adapted from the German literature as many other tech novelties of that time were), also used in current Russian literature by the names "Метод креста" ("Cross method"); "Конверт Пирсона" ("Pearson's envelope") or "Диагональная схема правила смешения" ("Diagonal mixing rule scheme").

share|improve this answer

edited 1 hour ago

answered 1 hour ago

andseliskandselisk

18.3k656121

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Very interesting and thanks for sharing this info. I have always been in favor of learning another language besides English for scientific purposes. English is my second language. I am writing one article for the Journal of Chemical Education on the utility of foreign languages in literature search. Your point provides another motivation to finish that article soon.
  $endgroup$
  – M. Farooq
  1 hour ago
  

  
  
  
  

add a comment | 

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3

$begingroup$

This is a so-called Pearson's square or Box method of balancing ratios, and not only chemical ones.

Widely popularized in Soviet books for analytical chemistry at least since 1940s (probably adapted from the German literature as many other tech novelties of that time were), also used in current Russian literature by the names "Метод креста" ("Cross method"); "Конверт Пирсона" ("Pearson's envelope") or "Диагональная схема правила смешения" ("Diagonal mixing rule scheme").

share|improve this answer

edited 1 hour ago

answered 1 hour ago

andseliskandselisk

18.3k656121

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Very interesting and thanks for sharing this info. I have always been in favor of learning another language besides English for scientific purposes. English is my second language. I am writing one article for the Journal of Chemical Education on the utility of foreign languages in literature search. Your point provides another motivation to finish that article soon.
  $endgroup$
  – M. Farooq
  1 hour ago
  

  
  
  
  

add a comment | 

3

$begingroup$

This is a so-called Pearson's square or Box method of balancing ratios, and not only chemical ones.

Widely popularized in Soviet books for analytical chemistry at least since 1940s (probably adapted from the German literature as many other tech novelties of that time were), also used in current Russian literature by the names "Метод креста" ("Cross method"); "Конверт Пирсона" ("Pearson's envelope") or "Диагональная схема правила смешения" ("Diagonal mixing rule scheme").

share|improve this answer

edited 1 hour ago

answered 1 hour ago

andseliskandselisk

18.3k656121

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Very interesting and thanks for sharing this info. I have always been in favor of learning another language besides English for scientific purposes. English is my second language. I am writing one article for the Journal of Chemical Education on the utility of foreign languages in literature search. Your point provides another motivation to finish that article soon.
  $endgroup$
  – M. Farooq
  1 hour ago
  

  
  
  
  

add a comment | 

$begingroup$

This is a so-called Pearson's square or Box method of balancing ratios, and not only chemical ones.

Widely popularized in Soviet books for analytical chemistry at least since 1940s (probably adapted from the German literature as many other tech novelties of that time were), also used in current Russian literature by the names "Метод креста" ("Cross method"); "Конверт Пирсона" ("Pearson's envelope") or "Диагональная схема правила смешения" ("Diagonal mixing rule scheme").

share|improve this answer

edited 1 hour ago

answered 1 hour ago

andseliskandselisk

18.3k656121

$endgroup$

share|improve this answer

edited 1 hour ago

answered 1 hour ago

andseliskandselisk

18.3k656121

answered 1 hour ago

andseliskandselisk

18.3k656121

answered 1 hour ago

andseliskandselisk

18.3k656121