1996-2-9-td
The theoretical minimum work required to separate one mole of a liquid mixture at 1 atm, containing 50 mole % each of n-heptane and n-octane into pure compounds each at 1 atm is
2002-1-22-td The partial molar enthalpy of a component in an ideal binary gas mixture of composition \(z\), at a temperature \(T\) and pressure \(P\), is a function only of
2003-6-td
When dilute aqueous solutions of two salts are mixed, the process is associated with
2004-8-td As pressure approaches zero, the ratio of fugacity to pressure (\(f/P\)) for a gas approaches
2007-9-td If \(m_i, \overline {m}_i, m_i^R, m_i^E\) are molar, partial molar, residual and excess properties respectively for a pure species “\(i\)”, the mixture property \(M\) of a binary non-ideal mixture of components 1 and 2, is given by
2011-13-td The partial molar enthalpies of mixing (in J/mol) for benzene (component 1) and cyclohexane (component 2) at 300 K and 1 bar are given by \(\Delta \bar {H_1} = 3600 x_2^2\) and \(\Delta \bar {H_2}=3600 x_1^2\), where \(x_1\) and \(x_2\) are the mole fractions.
When one mole of benzene is added to two moles of cyclohexane, the enthalpy change (in J) is
2011-9-td Minimum work \((W)\) required to separate a binary gas mixture at a temperature \(T_0\) and pressure \(P_0\) is \[ W = -RT_0 \left [ y_1\ln \left (\frac {\hat {f_1}}{f_{\text {pure,1}}}\right ) + y_2 \ln \left (\frac {\hat {f_2}}{f_{\text {pure,2}}}\right
) \right ] \] where \(y_1\) and \(y_2\) are mole fractions, \(f_{\text {pure,1}}\) and \(f_{\text {pure,2}}\) are fugacities of pure species at \(T_0\) and \(P_0\), and \(\hat {f_1}\) and \(\hat {f_2}\) are fugacities of species in the mixture at
\(T_0, P_0\) and \(y_1\). If the mixture is ideal then \(W\) is
1993-6-7-td A rigid insulated cylinder has two compartments separated by a thin membrane. While one compartment contains 1 kmol nitrogen at a certain temperature and pressure, the other contains 1 kmol of \(\ce {CO2}\) at the same temperature and pressure. The membrane
is ruptured and the two gases are allowed to mix. Assume that the gases behave as ideal gases. Calculate the increase in entropy (J/K) of the contents of the cylinder. Universal gas constant \(R = 8314\) J/kmol.K
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 ____________
2008-35-td The molar volume (\(V\)) of a binary mixture, of species 1 and 2 having mole fractions \(x_1\) and \(x_2\) respectively is given by \[ V = 220 x_1 + 180 x_2 + x_1x_2(90x_1+50x_2) \] The partial molar volume of species 2 at \(x_2=0.3\) is
2010-31-td At constant \(T\) and \(P\), the molar density of binary mixture is given by \(\rho =1+x_2\), where \(x_2\) is the mole fraction of component 2. The partial molar volume at infinite dilution for component 1, \(\bar {V_1}^\infty \), is
2012-31-td Consider a binary liquid mixture at constant temperature \(T\) and pressure \(P\). If the enthalpy change of mixing, \(\Delta H = 5 x_1 x_2\), where \(x_1\) and \(x_2\) are the mole fraction of species 1 and 2 respectively, and the entropy change of mixing
\(\Delta S = -R[x_1\ln x_1 + x_2 \ln x_2]\) (with \(R=8.314\) J/mol.K), then the minimum value of the Gibbs free energy change of mixing at 300 K occurs when
2015-32-td Given that molar residual Gibbs free energy, \(G^{\text {R}}\), and molar residual volume, \(V^{\text {R}}\), are related as \(\displaystyle \frac {G^{\text {R}}}{RT} = \int _0^P\left (\frac {V^{\text {R}}}{RT}\right )dP\), find \(G^{\text {R}}\) at \(T=27\)oC
and \(P=0.2\) MPa. The gas may be assumed to follow the virial equation of state, \(Z=1+BP/RT\), where \(B=-10^{-4}\) m3/mol at the given conditions. (\(R=8.314\) J/mol.K). The value of \(G^{\text {R}}\) in J/mol is:
2013-31-td A binary liquid mixture is in equilibrium with its vapor at a temperature \(T = 300\) K. The liquid mole fraction \(x_1\) of species 1 is 0.4 and the molar excess Gibbs free energy is 200 J/mol. The value of the universal gas constant is 8.314 J/mol.K,
and \(\gamma _i\) denotes the liquid-phase activity coefficient of species \(i\). If \(\ln (\gamma _1) = 0.09\), then the value of \(\ln (\gamma _2)\), up to 2 digits after the decimal point, is ____________
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 ____________
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.
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 ____________
1988-16-ii-td At 30\(^\circ \)C and 1 atm, the volumetric data for a liquid mixture of benzene(\(1\)) and cyclo-benzene(\(2\)) are represented by the equation \[ V (\text { cm\(^3\)/gmol}) = 109.4 - 16.8x_1 - 2.64x_1^2 \] where \(x_1\) is the mole fraction of benzene.
Find an expression for the partial molar volumes of the two components \(\bar {V}_1\) and \(\bar {V}_2\).
1990-6-i-td
Isothermal mixing of pure gases always produces a decrease in the --------------- . Hence work has to be done --------------- the system for separating a mixture of gases into its components.
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