1.10.35: Gibbs Energies- Liquid Mixtures- Immiscibility
- Page ID
- 386453
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)For a given binary liquid mixture (at defined \(\mathrm{T}\) and \(\mathrm{p}\)) characterised by a plot of excess Gibbs energy \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) against mole fraction, \({\mathrm{G}_{\mathrm{m}}}^{\mathrm{E}}\) can be positive. Indeed if \(\left[\mathrm{G}_{\mathrm{m}}^{\mathrm{E}} / \mathrm{R} \, \mathrm{T}\right]\) strongly exceeds 0.5, the mixture is partially miscible. That is to say the liquid comprises two liquid phases having different mole fraction compositions.
A fascinating variety of patterns emerge in the context of partial miscibilities.
- Some binary liquid mixtures are completely miscible but become partially miscible with increase in temperature. The corresponding miscibility curve has a minimum at a Lower Critical Solution Temperature, LCST. For example in the case of 2-butoxyethanol + water , the LCST is at \(322.2 \mathrm{~K}\) where \(x\left(\mathrm{H}_{2}\mathrm{O}\right)=0.942\) [1]. In fact all commonly quoted examples of this class of systems have water as one component. A fascinating example concerns propionitrile+ polystyrene mixtures. The miscibility curves indicate that the LCST occurs at negative pressures; in effect when the mixture is ‘stretched’ [2].
- Many binary liquid mixtures (e.g/ phenol + water has (at ambient pressure).are partially miscible, becoming completely miscible on raising the temperature. The miscibility curve has a maximum at an Upper Critical Solution Temperature, UCST. At ambient pressure a small number of liquid mixtures exhibit both UCST and LCST. In other words the miscibility plot forms a closed loop.
Partial miscibility plots also show deuterium isotope effects. In the case of \(\mathrm{CH}_{3}\mathrm{CN}+\mathrm{H}_{2}\mathrm{O} \left(\text{component } 2 = \mathrm{~CH}_{3}\mathrm{CN}\right)\) the UCST is \(272.10 \mathrm{~K}\) at \(x_{2}=0.38\) [2].
Footnotes
[1] A. Imre and W.A. Van Hook, J. Polym Sci.; Part B; Polymer Physics,1994,32,2283.
[2] M. J. Blandamer, M. J. Foster and D. Waddington, Trans. Faraday Soc.,1970,66,1369.