<p>Azeotropes are constant-boiling mixtures in which the liquid and vapor phases share the same composition. Previous work on the water–ethanol system proposed that, at the azeotropic condition, water and ethanol exhibit identical diffusion distributions as a dynamical signature. However, whether this dynamical behavior plays a causal role in azeotrope formation remains unresolved. In this work, we performed computational estimations of key thermodynamic quantities to probe the origin of the azeotropic behavior in the water–ethanol mixture at the azeotropic composition and temperature. We examined the composition dependence of the total Gibbs free energy of mixing (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Delta {\overline{G} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>G</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>) and found no distinctive feature at the azeotropic composition. A similar non-unique trend is observed for the entropic contribution (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Delta {\overline{S} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>S</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>). In contrast, the enthalpy of mixing (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Delta {\overline{H} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>H</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>) exhibits a distinctive signature at the azeotropic point compared to other compositions at the same temperature (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({T}_{\text{a}\text{z}\text{e}}= 351 \, \text{K}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>T</mi> <mtext>aze</mtext> </msub> <mo>=</mo> <mn>351</mn> <mspace width="0.166667em" /> <mtext>K</mtext> </mrow> </math></EquationSource> </InlineEquation>). It is observed that, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\Delta {\overline{H} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>H</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> remains negative until the azeotropic composition is crossed, after which it abruptly changes to become positive. This enthalpic signature underscores the critical importance of intermolecular interactions in establishing the unique azeotropic condition for water–ethanol mixture, though the universality of this feature is not tested.</p> Graphical abstract <p>In search of any thermodynamic signature at the azeotropic condition (<i>X</i><sub>aze</sub>, <i>T</i><sub>aze</sub>), computational calculation of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\Delta {\overline{{G}} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>G</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\Delta {\overline{{S}} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>S</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\Delta {\overline{{H}} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>H</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> is carried out. Neither <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\Delta {\overline{{G}} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>G</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> nor <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\Delta {\overline{{S}} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>S</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> exhibited any anomalous behavior. Interestingly, <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\Delta {\overline{{H}} }_{\text{m}\text{i}\text{x}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mover> <mi>H</mi> <mo>¯</mo> </mover> <mtext>mix</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> gives composition-dependent signature as it shows abrupt change on crossing <i>X</i><sub>aze</sub>, suggesting crucial role of intermolecular interactions.</p> <p></p>

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Thermodynamic origin of azeotropic condition: Composition dependent enthalpic signature in water–ethanol mixtures

  • Rik N Mukherjee,
  • Pradip K Ghorai,
  • Ranjit Biswas

摘要

Azeotropes are constant-boiling mixtures in which the liquid and vapor phases share the same composition. Previous work on the water–ethanol system proposed that, at the azeotropic condition, water and ethanol exhibit identical diffusion distributions as a dynamical signature. However, whether this dynamical behavior plays a causal role in azeotrope formation remains unresolved. In this work, we performed computational estimations of key thermodynamic quantities to probe the origin of the azeotropic behavior in the water–ethanol mixture at the azeotropic composition and temperature. We examined the composition dependence of the total Gibbs free energy of mixing ( \(\Delta {\overline{G} }_{\text{m}\text{i}\text{x}}\) Δ G ¯ mix ) and found no distinctive feature at the azeotropic composition. A similar non-unique trend is observed for the entropic contribution ( \(\Delta {\overline{S} }_{\text{m}\text{i}\text{x}}\) Δ S ¯ mix ). In contrast, the enthalpy of mixing ( \(\Delta {\overline{H} }_{\text{m}\text{i}\text{x}}\) Δ H ¯ mix ) exhibits a distinctive signature at the azeotropic point compared to other compositions at the same temperature ( \({T}_{\text{a}\text{z}\text{e}}= 351 \, \text{K}\) T aze = 351 K ). It is observed that, \(\Delta {\overline{H} }_{\text{m}\text{i}\text{x}}\) Δ H ¯ mix remains negative until the azeotropic composition is crossed, after which it abruptly changes to become positive. This enthalpic signature underscores the critical importance of intermolecular interactions in establishing the unique azeotropic condition for water–ethanol mixture, though the universality of this feature is not tested.

Graphical abstract

In search of any thermodynamic signature at the azeotropic condition (Xaze, Taze), computational calculation of \(\Delta {\overline{{G}} }_{\text{m}\text{i}\text{x}}\) Δ G ¯ mix , \(\Delta {\overline{{S}} }_{\text{m}\text{i}\text{x}}\) Δ S ¯ mix and \(\Delta {\overline{{H}} }_{\text{m}\text{i}\text{x}}\) Δ H ¯ mix is carried out. Neither \(\Delta {\overline{{G}} }_{\text{m}\text{i}\text{x}}\) Δ G ¯ mix nor \(\Delta {\overline{{S}} }_{\text{m}\text{i}\text{x}}\) Δ S ¯ mix exhibited any anomalous behavior. Interestingly, \(\Delta {\overline{{H}} }_{\text{m}\text{i}\text{x}}\) Δ H ¯ mix gives composition-dependent signature as it shows abrupt change on crossing Xaze, suggesting crucial role of intermolecular interactions.