Euler characteristic and Molar concentration: Difference between pages

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The '''Euler characteristic''' of a [[shape]] is a [[number]] that describes a [[topological space]], so that anything in the space will have the same number.
'''Molar concentration''', or '''molarity''', or simply [[concentration]], is a term in [[physical chemistry]]. It measures the concentration of a [[solution]] or [[mixture]].
It is calculated by taking the number of [[Point (geometry)|points]] in the shape, the number of [[line]]s in the shape, and the number of [[wikt:face|faces]] of the shape. Then, you find the Euler characteristic with this formula:


:<math>\chi=V-E+F \,\!</math>
In chemistry, the '''molar concentration''', <math>c_i</math> is defined as the [[amount of substance|amount]] of a constituent <math>n_i</math> (usually measured in [[Mole (unit)|moles]]&nbsp;– hence the name) divided by the [[volume]] of the mixture <math>V</math>:<ref name="GoldBook"> [[International Union of Pure and Applied Chemistry]]. Amount concentration, c. ''Compendium of chemical terminology'', internet edition. [http://goldbook.iupac.org/A00295.html]</ref>
V is the point count, E the line count, and F the amount of faces. For most common shapes, the Euler Characteristic is 2.


{| class="wikitable"
:<math>c_i = \frac {n_i}{V}</math>
|-
!Name
!Image
!Vertices (Points)<BR>''V''
!Edges (Lines)<BR>''E''
!Faces <BR>''F''
!Euler characteristic:<BR>''V'' &minus; ''E'' + ''F''
|- align=center
|[[Tetrahedron]]
|[[File:tetrahedron.png|50px]]
|4
|6
|4
|'''2'''
|- align=center
|[[Hexahedron]] or [[cube (geometry)|cube]]
|[[File:hexahedron.png|50px]]
|8
|12
|6
|'''2'''
|- align=center
|[[Octahedron]]
|[[File:octahedron.png|50px]]
|6
|12
|8
|'''2'''
|- align=center
|[[Dodecahedron]]
|[[File:dodecahedron.png|50px]]
|20
|30
|12
|'''2'''
|- align=center
|[[Icosahedron]]
|[[File:icosahedron.png|50px]]
|12
|30
|20
|'''2'''
|}


[[Category:Mathematics]]
The volume <math>V</math> in the definition <math>c_i = n_i/V</math> refers to the volume of the [[solution]], ''not'' the volume of the [[solvent]]. One litre of a solution usually contains either slightly more or slightly less than 1 [[litre]] of solvent because when a substance dissolves in a solvent it causes volume of liquid to increase or decrease.


{{math-stub}}
The [[reciprocal]] quantity represents the [[dilution]] (volume) which can appear in Ostwald's [[law of dilution]].
 
== References ==
{{reflist}}
 
 
{{chem-stub}}
 
 
[[Category:Physical chemistry]]

Latest revision as of 20:06, 12 October 2014

Molar concentration, or molarity, or simply concentration, is a term in physical chemistry. It measures the concentration of a solution or mixture.

In chemistry, the molar concentration, [math]\displaystyle{ c_i }[/math] is defined as the amount of a constituent [math]\displaystyle{ n_i }[/math] (usually measured in moles – hence the name) divided by the volume of the mixture [math]\displaystyle{ V }[/math]:[1]

[math]\displaystyle{ c_i = \frac {n_i}{V} }[/math]

The volume [math]\displaystyle{ V }[/math] in the definition [math]\displaystyle{ c_i = n_i/V }[/math] refers to the volume of the solution, not the volume of the solvent. One litre of a solution usually contains either slightly more or slightly less than 1 litre of solvent because when a substance dissolves in a solvent it causes volume of liquid to increase or decrease.

The reciprocal quantity represents the dilution (volume) which can appear in Ostwald's law of dilution.

References

Template:Reflist


Template:Chem-stub

  1. ↑ International Union of Pure and Applied Chemistry. Amount concentration, c. Compendium of chemical terminology, internet edition. [1]
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