Rule of conodes

The Konoden rule (also known as the law of lever arms and the law of the lever arms turned away ) is a term used in thermodynamics to describe phases . If there is a liquid two-component system (mixture of substance A and B) of liquids that are not completely miscible in one another in a two-phase area (I + II) (see phase diagram ), then phase I, consisting mainly of substance A, is completely saturated with substance B and Conversely, phase II, consisting of substance B, completely saturated with substance A.

${\displaystyle V_{\text{I}}\cdot (c_{0}-c_{\text{I}})=V_{\text{II}}\cdot (c_{\text{II}}-c_{0})}$

V _{I / II} = volume of phase I / II [cm ³ ]

c _{I / II} = concentration of substance A in the volume of phase I / II [ mol / cm ⁻³ ]

c ₀ = total concentration of substance A in the volume of phases I and II [mol / cm ⁻³ ]

The definition of the rule of conodes on the proportions of substance quantities is equivalent :

${\displaystyle n_{\text{I}}\cdot (x_{0}-x_{\text{I}})=n_{\text{II}}\cdot (x_{\text{II}}-x_{0})}$

n _{I / II} = amount of substance A and B in phase I / II

x ₀ = proportion of substance A in the overall system (phase I and II)

x _{I / II} = mole fraction of substance A in phase I / II

Derivation

The total volume of the mixture V ₀ is the sum of the volumes of phases I and II:

${\displaystyle V_{0}=V_{\text{I}}+V_{\text{II}}}$

Multiplying by the total concentration results in an equation for the total amount n _{A, 0} of substance A:

${\displaystyle n_{{\text{A}},0}=V_{0}\cdot c_{0}=V_{\text{I}}\cdot c_{0}+V_{\text{II}}\cdot c_{0}}$

Furthermore, the total amount n _{A, 0} of substance A must be retained, even if it is divided into phases I and II:

${\displaystyle V_{0}\cdot c_{0}=V_{\text{I}}\cdot c_{\text{I}}+V_{\text{II}}\cdot c_{\text{II}}}$

By equating these two equations, the above-mentioned equation results, which also applies to substance B in an analogous manner.

From the maintenance of the total amount of substance also follows that the sum of the individual concentrations c _I and c _II of compound A is not approximately equal to the total concentration c ₀ rather is, but:

${\displaystyle c_{0}={\frac {V_{\text{I}}}{V_{0}}}\cdot c_{\text{I}}+{\frac {V_{\text{II}}}{V_{0}}}\cdot c_{\text{II}}}$

literature

• PW Atkins: Physical Chemistry . 3. corr. Edition. VCH , Weinheim 2001, p. 233 f .

• Georg Job, Regina Rüffler: Physical Chemistry An introduction based on a new concept with numerous experiments . 1st edition. Vieweg + Teubner Verlag , Wiesbaden 2011, p. 318 .