1.14.32: Hildebrand Solubility Parameter
- Page ID
- 386960
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The cohesive energy density (c.e.d.) of a liquid is defined by equation (a).
\[\text { c.e.d. }=\Delta_{\text {vap }} \mathrm{U}^{0} / \mathrm{V}^{*}(\ell) \nonumber \]
\(\Delta_{\text {vap }} \mathrm{U}^{0}\) is the change in thermodynamic energy when one mole of a given chemical substance passes from the liquid to the vapor state. The square root of the c.e.d. for liquid \(j\) is the Hildebrand solubility parameter for that liquid.
\[\delta=(\text { c.e.d. })^{1 / 2} \nonumber \]
\(\delta\) can be expressed in many units but following the original definition the customary unit is \(\left(\mathrm{cal}^{1 / 2} \mathrm{~cm}^{-3 / 2}\right)\). Property \(\delta\) provides an estimate of cohesion within a given liquid. The idea goes a little further in terms of understanding solubilities. A clever idea is based on the following argument.
Consider two liquids \(\mathrm{A}\) and \(\mathrm{B}\). We want to take a small sample of liquid \(\mathrm{A}\) (as a solute) and dissolve in liquid \(\mathrm{B}\) as the solvent. Within liquid \(\mathrm{A}\) the intermolecular interactions \(\mathrm{A} \ldots \(\mathrm{A}\) are responsible for the cohesion within this chemical substance. Similarly within liquid \(\mathrm{B}\), \(\mathrm{B} - \mathrm{~B}\) intermolecular forces are responsible for the cohesion within liquid \(\mathrm{B}\). If \(\mathrm{B} - \mathrm{~B}\) interactions are much stronger than \(\mathrm{A} - \mathrm{~A}\) and \(\mathrm{A} - \mathrm{~B}\) intermolecular interactions it is likely that \(\mathrm{A}\) will not be soluble in liquid \(\mathrm{B}\). Similarly if \(\mathrm{A} - \mathrm{~A}\) interactions are stronger than \(\mathrm{B} - \mathrm{~B}\) and \(\mathrm{A} - \mathrm{~B}\) interactions it is likely that \(\mathrm{A}\) will not be soluble in liquid \(\mathrm{B}\). If substance \(\mathrm{A}\) is to be soluble in liquid \(\mathrm{B}\), their cohesive energy densities should be roughly equal.