Excess volume

The excess volume V ^E is the difference between the real volume of a mixture of chemical substances and the ideal volume, which corresponds to the sum of the volumes of the components before mixing ( pure substance volumes):

${\displaystyle V^{E}=V_{\text{Gemisch}}-\sum V_{\text{Reinstoffe}}}$

If the volume of the real mixture is greater than that of the ideal, the excess volume is positive (volume dilation), in the opposite case it is negative ( volume contraction ). As the difference between the real and ideal behavior of a mixture, the excess volume is an excess quantity .

Excess molar volume

In relation to the amount of substance  n in the mixture, one speaks of the molar excess volume :

${\displaystyle V_{m}^{E}={\frac {V^{E}}{n}}={\frac {V_{\text{Gemisch}}-\sum V_{\text{Reinstoffe}}}{n}}={V_{m}}_{\text{Gemisch}}-\sum {V_{m}}_{\text{Reinstoffe}}.}$

The molar volume of the mixture is equal to the sum of the partial molar volumes of the components:

${\displaystyle {\begin{aligned}{V_{m}}_{\text{Gemisch}}&=\sum {V_{m}}_{\text{Komponente}}\\\Leftrightarrow {\frac {V_{\text{Gemisch}}}{n}}&=\sum {\frac {V_{\text{Komponente}}}{n}}\end{aligned}}}$

The partial molar volume of a substance A is the volume that this substance contributes as a component to the total volume of a mixture of several substances A and B. It depends both on the other substance B and on the mixing ratio and is not always identical to the molar volume that substance A occupies as a pure substance:

${\displaystyle {V_{m}}_{\text{Komponente}}={\frac {V_{\text{Komponente}}}{n}}=f({\text{Mischung}})\neq {V_{m}}_{\text{Reinstoff}}={\frac {V_{\text{Reinstoff}}}{n}}={\frac {M}{\rho }}}$

With

• Molar mass  M and
• Density . ${\displaystyle \rho }$

Scale and examples

The volume effect of mixing pure substances is relatively small. Usually the difference is only around one to two percent.

• Mixtures of non-polar and polar substances usually show a clearly positive excess volume, i.e. H. the volume of the mixture is greater than that of the ideal mixture (volume dilatation). Examples are:
  

  Di-n-propyl ether / heptane
  • Methylcyclohexane and 2-pentanol (maximum = +0.50 cm ³ / mol at = 117.98 cm ³ / mol, 298 K = 25 ° C) ${\displaystyle V_{m}^{E}}$ ${\displaystyle V_{m}}$
  • Dichloromethane and 2-butanone (maximum = +0.06 cm ³ / mol at = 72.99 cm ³ / mol, 298 K = 25 ° C) ${\displaystyle V_{m}^{E}}$ ${\displaystyle V_{m}}$

• Mixtures of small polar components and larger molecules with a polar group often have a negative excess volume, i.e. H. the volume is smaller than that of the ideal mixture ( volume contraction ). Examples are:
  

  Tetrahydrofuran / water
  • N-methyl-2-oxazolidinone and water (minimum = −0.54 cm ³ / mol, 298 K = 25 ° C) ${\displaystyle V_{m}^{E}}$
  • Pyridine and methanol (minimum = −0.48 cm ³ / mol at = 57.53 cm ³ / mol, 298 K = 25 ° C) ${\displaystyle V_{m}^{E}}$ ${\displaystyle V_{m}}$
  • Carbon monoxide and methane (minimum = −0.35 cm ³ / mol at = 36.29 cm ³ / mol, 90 K = −183 ° C) ${\displaystyle V_{m}^{E}}$ ${\displaystyle V_{m}}$

See also

• Activity coefficient
• Mixed heat
• Volume ratio
• Volume concentration
• Volume fraction

swell

1. ↑ Dortmund database
2. ↑ Dortmund database

Web links

Commons : Excess volume diagrams  - collection of images, videos and audio files