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Solutions – fundamentals - Ideal solutions

Q: What does <img class='fmath-formula' src='data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAAnCAYAAAARrli9AAABLElEQVR42u2WAQ2DMBBFKwEJSEACEpCABCQgAQlIQAISkIAEHHR5zf5CGGxsO1hIegmhobSvd+2/nvMnmbOeME1T3zTNMaC+7/0wDKGd57nvus5P0xSA4zjagZg8SZIAq+s6fCvL0jvnwiJMQ8fKmRRA27YPgPke4Q2hKooivBU+U1CWZSF0TEzo8E6h0945K2+06UDxRodEXl3reP9FsBF0cRAaQGgS25qpf5laPgIxGBXPk+DTj/d+Jc0IiqAIsgdxB9G/JfgnEIXFKSBKp7X0swRVVfVb6ARTblOb4oM+3tQFW57vBnHnq82kuv8po/R9yxvgu0NHW898ENXMvPSdG1WPFrh5mPaeunemfYyg40Hf2m6QdHMoyMLQ1ssUZgFBR4oIz5rWTqvrbpKiNL4EsG9GAAAAAElFTkSuQmCC' latex='$mu^*_i$'> ,from the ideal solution model, in a real system represent at the near-pure limit?

When x i --> 1 it gives the chemical potential for a single-component system i at T and P. When x i --> 0 it gives the chemical potential of a hypothetical state of infinite dilution. It is then dependent on the solvent.

7 important questions on Solutions – fundamentals - Ideal solutions

By what properties is an ideal solution defined?

1. There is no interaction between any of the components.
2. Th ideal entropy of mixing contributes to the total entropy, at constant pressure and temperature.
3. Ideal solutions are a prediction of the behaviour of near pure solutions, with one major component and very small concentrations of other components.

In a lattice mixing model, how is the number of configurations predicted?

The number of arrangements of N_A A particles and N_B B particles in the N = N_A + N_B sites is given by the formula:

A sterling's approximation is applied in the second line.

How can the ideal mixing entropy for a binary mixture be expressed in x_A?

with x_A the mole fraction of A. and k_B the Boltzmann constant.

How can the mixing entropy be expressed for a C component mixture?

Which is the same as for ideal gasses.

What do the terms in this equation represent?

Looking at the right hand side of the equation, the first term is the Gibbs free energy in pure state for each of the components. The second term is negative to make sure the mixing entropy is greater than the entropy of the pure components.

How is the chemical potential of component i after mixing in an ideal solution derived?

The first term on the second line becomes

. This is the chemical potential of the pure component i.
The right term on the second line becomes

, which is always negative since x_i<0.
This means that the chemical potential decreases during mixing.

What does ,from the ideal solution model, in a real system represent at the near-pure limit?

When x_i --> 1 it gives the chemical potential for a single-component system i at T and P.
When x_i --> 0 it gives the chemical potential of a hypothetical state of infinite dilution. It is then dependent on the solvent.

The question on the page originate from the summary of the following study material:

Thermodynamics and Statistical Mechanics An Integrated Approach | 9781316123324 | M Scott Shell

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