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  • General

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    • Overview of GATE Chemical Engineering Page
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  • Solution Thermodynamics

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    • Quick Review of Theory Page
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    • Entropy Change of Mixing of Ideal Gases Page
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    • Entropy Change of Mixing of Ideal Solution Page
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    • Work for Separating a Mixture Page
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    • Molar Property of Solution Page
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    • Partial Molar Enthalpy of Ideal Gas Mixture Page
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    • Volumes of Individual Components for Mixture Page
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    • Partial Molar Volume Page
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    • Partial Molar Volume from Density Page
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    • Volume Change of Mixing Page
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      2019-38-td

      For a given binary system at constant temperature and pressure, the molar volume (in m3/mol) is given by: \(V=30x_A+20x_B+x_Ax_B(15x_A-7x_B)\), where \(x_A\) and \(x_B\) are the mole fractions of components \(A\) and \(B\), respectively. The volume change of mixing \(\Delta V_{\text {mix}}\) (in m3/mol) at \(x_A=0.5\) is ____________
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    • Partial Molar Enthalpy at Infinite Dilution Page
      2016-5-td
      The partial molar enthalpy (in kJ/mol) of species 1 in a binary mixture is given by \(\bar {H}_1=2-60x_2^2+100x_1x_2^2\), where \(x_1\) and \(x_2\) are the mole fractions of species 1 and 2, respectively. The partial molar enthalpy (in kJ/mol, rounded off to the first decimal place) of species 1 at infinite dilution is ____________
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    • Molar Properties of Solution from Tabular Data Page
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    • Variation of Residual Gibbs Free Energy Page
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    • Residual Enthalpy from Equation of State Page
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    • Fugacity at Low Pressure Page
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    • Fugacity of Gas from Virial Equation Page
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    • Fugacity from G Page
      2017-34-td
      The vapor pressure of a pure substance at a temperature \(T\) is 30 bar. The actual and ideal gas values of \(G/RT\) for the saturated vapor at this temperature \(T\) and 30 bar are 7.0 and 7.7, respectively. Here, \(G\) is the molar Gibbs free energy and \(R\) is the universal gas constant. The fugacity of the saturated liquid at these conditions, rounded to 1 decimal place, is ____________bar.
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    • G/RT of Solution Page
      2016-34-td
      A binary system at a constant pressure with species `1' and '2' is described by the two-suffix Margules equation, \(\displaystyle \frac {G^E}{RT}=3x_1x_2\), where \(G^E\) is the molar excess Gibbs free energy, \(R\) is the universal gas constant, \(T\) is the temperature and \(x_1\), \(x_2\) are the mole fractions of species 1 and 2, respectively. At a temperature \(T\), \(\dfrac {G_1}{RT} = 1\) and \(\dfrac {G_2}{RT} = 2\), where \(G_1\) and \(G_2\) are the molar Gibbs free energies of pure species 1 and 2, respectively. At the same temperature, \(G\) represents the molar Gibbs free energy of the mixture. For a binary mixture with 40 mole% of species 1, the value (rounded off to the second decimal place) of \(\dfrac {G}{RT}\) is ____________
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    • Activity Coefficient and Excess Gibbs Free Energy Page
      2020-19-td
      Mole fraction and activity coefficient of component 1 in a binary liquid mixture are \(x_1\) and \(\gamma _1\) respectively. \(G^{\text {E}}\) is excess molar Gibbs energy of the mixture, \(R\) is universal gas constant and \(T\) is absolute temperature of the mixture. Which one of the following is always true?
      1. \(\displaystyle \lim _{x_1\rightarrow 1}\frac {G^{\text {E}}}{RT}=0.5\)
      2. \(\displaystyle \lim _{x_1\rightarrow 1}\gamma _1=0\)
      3. \(\displaystyle \lim _{x_1\rightarrow 1}\frac {G^{\text {E}}}{RT}=0\)
      4. \(\displaystyle \lim _{x_1\rightarrow 1}\gamma _1=0.5\)
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    • Activity Coefficients from Expression of GE/RT Page
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    • Slope of Activity Coefficient vs Composition Curve Page
      2021-40-td
      A binary liquid mixture consists of two species 1 and 2. Let \(\gamma \) and \(x\) represent the activity coefficient and the mole fraction of the species, respectively. Using a molar excess Gibbs free energy model, \(\ln \gamma _1\) vs. \(x_1\) curve at a mole fraction of \(x_1=0.2\) has a slope of \(-1.728\).

      The slope of the tangent drawn to the \(\ln \gamma _2\) vs. \(x_1\) curve at the same mole fraction is ________ (correct to 3 decimal places).

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