Van't Hoff factor

In physical chemistry , the dimensionless Van-'t-Hoff factor i denotes the ratio that forms the sum of the amount of substance of a dissolved substance (solute) in an aqueous solution with the amount of substance of the originally added starting material.

The factor is thus a measure of the extent to which the dissolved substance dissociates and - if it is at least partially dissociated - into how many particles it is divided into during dissociation. The name goes back to Jacobus Henricus van 't Hoff , the first winner of the Nobel Prize in Chemistry .

meaning

The Van-'t-Hoff factor plays an important role in colligative processes in particular , since it is the absolute number and not the type of particles that matter here. For example, the osmotic pressure of a saline solution is almost twice as high as that of a sugar solution with the same amount of substance concentration (see examples).

calculation

The following applies:

${\displaystyle i={\frac {\Sigma n_{\mathrm {geloest} }}{n_{0}}}}$

${\displaystyle \Leftrightarrow \Sigma n_{\mathrm {geloest} }=i\cdot n_{0}}$

• The dissociated part of the original amount of substance ( is the degree of dissociation ; ) may be divided into several particles when going into solution; this is taken into account by the following factor: ${\displaystyle \alpha \cdot n_{0}}$ ${\displaystyle \alpha }$ ${\displaystyle 0\leq \alpha \leq 1}$

${\displaystyle q={\frac {\Sigma n_{\mathrm {geloest} }}{n_{0}}}}$( assuming complete dissociation , i.e. ). ${\displaystyle \alpha =1}$

In other words, the factor q indicates how many moles 1 mole of the starting material would be divided into in the event of complete dissociation ( ). Due to the partial dissociation, they form in the solution ${\displaystyle q\geq 1}$

${\displaystyle n_{\mathrm {diss} }=q\cdot (\alpha \cdot n_{0})}$ Particle.

• Also, the non- dissociated proportion of the original amount of substance in the solution is counted ( the degree of association): ${\displaystyle 1-\alpha }$

${\displaystyle n_{\mathrm {ass} }=(1-\alpha )\cdot n_{0}.}$

The following applies:

${\displaystyle {\begin{aligned}\Rightarrow \Sigma n_{\mathrm {geloest} }&=n_{\mathrm {diss} }+n_{\mathrm {ass} }\\\Leftrightarrow i&=q\cdot \alpha +(1-\alpha )\end{aligned}}}$

${\displaystyle \Leftrightarrow i=1+\alpha (q-1).}$

Examples

As an example, glucose has a Van't Hoff factor of 1 because it is undissociated and soluble in water:

${\displaystyle {\begin{aligned}\alpha _{\mathrm {Glucose} }&=0\\\Rightarrow i_{\mathrm {Glucose} }&=1.\end{aligned}}}$

In contrast, the Van-'t-Hoff factor of sodium chloride is 2, because one mole of  NaCl dissociates almost completely into one mole each of Na ⁺ and Cl ^- :

${\displaystyle {\begin{aligned}n_{\mathrm {Na^{+}} }=n_{\mathrm {Cl^{-}} }=1\;\mathrm {mol} \Rightarrow q_{\mathrm {NaCl} }&=2\\\alpha _{\mathrm {NaCl} }&=1\\\Rightarrow i_{\mathrm {NaCl} }&=2.\end{aligned}}}$

Substances such as weak electrolytes , which only partially dissociate, have a broken Van't Hoff factor depending on the dissociation equilibrium .

swell

• Entry on Raoult's Laws. In: Römpp Online . Georg Thieme Verlag, accessed on December 18, 2014.