Non-ideal parameter

35

Mole Fraction A

0.50

Directions

Details

About

\( H_{A} \)

\( H_{B} \)

\( \overline{ H_{A} } \)

\( \overline{ H_{B} } \)

\( \overline{ H_{A} } = 59 \; \mathrm{ kJ / mol } \qquad \quad \overline{ H_{B} } = 79 \; \mathrm{ kJ / mol } \)

The molar enthalpy of a binary mixture (blue curve) of A and B is plotted as a function of the mole fraction of component A. The end points of the molar enthalpy are the pure-component enthalpies \( H_{A} \) and \( H_{B} \). The partial molar enthalpies \( \overline{ H_{A} } \) and \( \overline{ H_{B} } \) are obtained by drawing a tangent line (black, dashed) at the black point, which indicates the mole fraction of the solution. The intersections of this tangent with the y-axis at x_{A} = 0 and x_{A} = 1 correspond to \( \overline{ H_{B} } \) and \( \overline{ H_{A} } \), respectively. You can change the mole fraction of A in the mixture and the non-ideal parameter, which represents deviation from an ideal solution, with sliders. For an ideal solution the non-ideal parameter is zero, and the enthalpy of the mixture is a linear function of the molar enthalpies of the pure components.

The molar enthalpy of a binary mixture \( H \) is:

$$ [1] \quad H = x_{A} H_{A} + x_{B} H_{B} + \alpha \, x_{A} x_{B} $$where \( H_{A} \) and \( H_{B} \) are the molar enthalpies of components \( A \) and \( B \). \( x_{A} \) and \( x_{B} \; \) are the mole fractions of \( A \) and \( B \), and \( \alpha \) is a non-ideal parameter. The partial molar enthalpies \( \overline{ H_{A} } \) and \( \overline{ H_{B} } \) are:

$$ [2] \quad \overline{ H_{ A } } = H + x_{B} \frac{ dH }{ dx_{A} } $$ $$ [3] \quad \overline{ H_{ B } } = H + x_{A} \frac{ dH }{ dx_{A} } $$The intercepts of a line drawn tangent to the molar enthalpy curve (blue) at a given mole fraction are the partial molar enthalpies (i.e., the intercept at \( x_{A} = 1 \) is the partial molar enthalpy of \( A \)).

References:

- 1.)
*Partial Molar Properties: Binary Solutions*[Video]. (Apr 5, 2012) www.youtube.com/watch?v=TFmIPEG_X3A.

This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Neil Hendren under the direction of Professor John L. Falconer. Address any questions or comments to learncheme@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.

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