# 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):

${\ displaystyle V ^ {E} = V _ {\ text {mixture}} - \ sum V _ {\ text {pure substances}}}$ 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 :

${\ displaystyle V_ {m} ^ {E} = {\ frac {V ^ {E}} {n}} = {\ frac {V _ {\ text {mixture}} - \ sum V _ {\ text {pure substances}} } {n}} = {V_ {m}} _ {\ text {mixture}} - \ sum {V_ {m}} _ {\ text {pure substances}}.}$ 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 {mixture}} & = \ sum {V_ {m}} _ {\ text {components}} \\\ Leftrightarrow {\ frac {V_ {\ text {mixture}}} {n}} & = \ sum {\ frac {V _ {\ text {components}}} {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:

${\ displaystyle {V_ {m}} _ {\ text {component}} = {\ frac {V _ {\ text {component}}} {n}} = f ({\ text {mixture}}) \ neq {V_ {m}} _ {\ text {pure substance}} = {\ frac {V _ {\ text {pure substance}}} {n}} = {\ frac {M} {\ rho}}}$ 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:
• 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:
• 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)${\ displaystyle V_ {m} ^ {E}}$ ${\ displaystyle V_ {m}}$ 