HardChemistryHigh School (11–12)Solutions › Colligative Properties and the van 't Hoff FactorNumerical

In benzene, ethanoic acid molecules can join in pairs…

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In benzene, ethanoic acid molecules can join in pairs. A solution of $1.20\ \text{g}$ of ethanoic acid, of molar mass $60\ \text{g/mol}$ , in $30.0\ \text{g}$ of benzene freezes $1.88\ \text{K}$ below pure benzene. Take $K_f = 5.12\ \text{K kg/mol}$ . Find the van’t Hoff factor and the fraction of the molecules that are in pairs.

Need a reminder? The key ideaShow

The van’t Hoff factor is $i = \dfrac{\text{observed effect}}{\text{calculated effect}}$ . For a solute that gives $\nu$ ions, $i = 1 + \alpha(\nu - 1)$ . For a solute that joins in pairs, $i = 1 - \dfrac{\alpha}{2}$ . Then $\Delta T_f = i\,K_f\,m$ and $\pi = i\,C\,R\,T$ .

The worked solution

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