Extending the M1 derivation of the activity coefficient to multicomponent mixtures (uakron.edu, 14min) is straightforward but requires careful attention to the meaning of the subscripts and notation. It is a good warmup for derivations of more sophisticated activity models. This presentation begins with a brief review of the M1 model and its relation to the Gibbs excess function, then systematically explains the notation as it extends from the binary case to multiple components.

Comprehension Questions 1. Derive the activity coefficient for the multicomponent M2 model. 2. Derive the activity coefficient for the multicomponent Redlich-Kister model.

Shows how to modify the spreadsheet created for Ideal Solutions (Section 10.4) to apply modified Raoult's law for 5 components using the M1/MAB model.

Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."

Comprehension Questions: 1. Find the bubble and dew pressures of an equimolar mixture of chloroform, acetone, and ethanol at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected? 2. Find the bubble and dew pressures of an equimolar mixture of acetone, ethanol, and methane at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected? 3. Find the bubble and dew pressures of an equimolar mixture of chloroform, acetone, and ethanol at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected? 4. Find the bubble and dew pressures of an equimolar mixture of acetone, ethanol, and methane at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected?

## Comments

Elliott replied on Permalink

## Derivation of Activity Coefficients: Multicomponent M1/MAB Model

Extending the M1 derivation of the activity coefficient to multicomponent mixtures (uakron.edu, 14min) is straightforward but requires careful attention to the meaning of the subscripts and notation. It is a good warmup for derivations of more sophisticated activity models. This presentation begins with a brief review of the M1 model and its relation to the Gibbs excess function, then systematically explains the notation as it extends from the binary case to multiple components.

Comprehension Questions

1. Derive the activity coefficient for the multicomponent M2 model.

2. Derive the activity coefficient for the multicomponent Redlich-Kister model.

Elliott replied on Permalink

## Implementation of the Multicomponent M1/MAB Model

## M1/MAB Extension of the Multicomponent Flash Spreadsheet (19min, uakron.edu) adapted from Ideal Solutions (cf Section 10.4)

Shows how to modify the spreadsheet created for Ideal Solutions (Section 10.4) to apply modified Raoult's law for 5 components using the M1/MAB model.

Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."

Comprehension Questions:

1. Find the bubble and dew pressures of an equimolar mixture of chloroform, acetone, and ethanol at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected?

2. Find the bubble and dew pressures of an equimolar mixture of acetone, ethanol, and methane at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected?

3. Find the bubble and dew pressures of an equimolar mixture of chloroform, acetone, and ethanol at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected?

4. Find the bubble and dew pressures of an equimolar mixture of acetone, ethanol, and methane at 5 bars using the MAB model. Then compute V/F x and y at the pressure that is halfway between dew and bubble. Is it what you expected?