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Hi Prof, I'm still a bit confused about what exactly fugacity is. I understand its uses like it can help to define other properties and the usefulness of the fugacity coefficient or activity coefficient, but what exactly is fugacity?

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Hi prof, I don't really understand why there is a need to multiply the partial molar enthalpy expressions with the corresponding composition of that species i.e. why do we need to do x1*100*(1+0.08x2^2)? I thought the x1 is accounted for in the partial molar enthalpy expression?

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Is there a Mr bar on top of the partial property equation as well? If not, why not?

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hi prof how do you tell the difference between two constant margules model vs van laar model just by looking at the graph given?

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Prof, for the equation highlighted, may I know why the limit of G^E/X1X2RT when Xi approaches 0 results in Gamma i infinity?

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Is there a way to determine whether G_E/RT graph has a local max/min?

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Is there a way to determine whether G_E/RT graph has a local max/min?

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In general, is there a simple way to determine whether G_E/RT has a local max/min simply based on the shape of the ln(gamma1) or ln(gamma2) graphs? I know that we can deduce this if we obtain a mathematical expression for G_E/RT in terms of x1. But suppose I don't obtain the expression for G_E/RT in terms of x1, is there any easy way to deduce this?

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2 pure component (1 and 2) mix to form y1 (0.75) and y2 (0.25) components.

Shouldn't H initial be only H1+H2 only? since the composition is 1 for pure species?

If we were to stick to this pattern then it should be n1 and n2 instead right?

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is there a situation where by Excess property is >0 but residual is =0? Since u must have interactions in the first place for it to be unequal 

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is there a situation where by Excess property is >0 but residual is =0? Since u must have interactions in the first place for it to be unequal 

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Comprises of two or more chemical species

Like (similar molecules) and unlike interactions (dissimilar molecule) exists

Like and unlike interactions are of different magnitude

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How to evaluate property of real mixture?

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How to evaluate property of real mixture?

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Use Ideal Gas mixture Model (or) Ideal Solution Model

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Property of mixture (Ideal Gas mixture state) + Residual property of mixture

Both the property evaluation should be done at real mixture P and T

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Property of mixture (Ideal Solution state) + Excess property of mixture

Both the property evaluation should be done at real mixture P and T

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Difference between property of mixture at Ideal Gas State (T,P) and property of mixture at real state (T,P)

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Describes deviation of a system from Ideal Gas behaviour.

Accounts for the all interactions among the molecules in the system

Exists if there is interaction among molecules (irrespective of like-/unlike-)

Does not exist if there is no interaction among molecules

Exists for pure species (At real state we can expect interaction among molecules based on the state of the system)

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Difference between property of mixture at Ideal Solution State (T,P) and property of mixture at real state (T,P)

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Describes deviation of a system from Ideal Solution behaviour.

Accounts for the interactions of different magnitude among the molecules in the system

Exists if like and unlike interaction among molecules are of different magnitude (irrespective of like-/unlike-)

Does not exist if the interaction among the molecules are the same (similar to pure species)

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Describes deviation from ideal gas behaviour

Defined for a specific species in a mixture

Not a partial molar property.

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Describes deviation from Ideal solution behaviour

Defined for a specific species in a mixture

Not a partial molar property.

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Ratio of fugacity of species in a real mixture to ratio of fugacity of species in the same mixture at an ideal gas mixture state (hypothetical)

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Ratio of fugacity of species in a real mixture to ratio of fugacity of species in the same mixture an ideal solution (hypothetical)

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For species in ideal solution, activity coefficient is one

Gamma i >1: Positive deviation from ideal solution (Like-like interactions are stronger)

Gamma i <1: Negative deviation from ideal solution (Unlike interactions are stronger)

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For species in ideal gas mixture fugacity coefficient of is one

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Natural Logarithm of fugacity coefficient is dimensionless partial residual Gibbs Free Energy (G R/RT)

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Natural Logarithm of activity coefficient is dimensionless partial excess Gibbs Free Energy (G E/RT)

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#Virial Coefficients Method

Equations of state

#Governing equations are provided for future reference. Evaluation methods will not be covered in this module

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Mixing Experiment

Low Pressure VLE experiment

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Mixing Experiment data is mathematically modeled to obtain excess volume and excess enthalpy property relation

Excess Volume of mixture
Volume of mixing pure species at constant T and P to form a mixture

Excess Enthalpy
Enthalpy of mixing pure species at constant T and P to form the mixture

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#Virial Coefficients Method (applicable to gaseous mixtures)
#Governing equations are provided for future reference.

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X i ---> 1

Activity coefficient of the species will be one

Fugacity of the species will be pure species fugacity (at mixture T,P)

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X i ---> 0

Activity coefficient of the species will be "Activity coefficient at infinite dilution". It is used as a model parameter in excess property relations

Fugacity of the species will be given by Henry's law. It is used to limited solubility of gases in liquid (VLE)

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Low Pressure VLE experiment data (Modified Raoult's Law)

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Excess Gibbs Free Energy
Low pressure VLE Experiment data is mathematically modeled to obtain excess Gibbs Free Energy
Example: Margules Equation, Van Laar Equations

Activity coefficient of species in a mixture
Using the excess Gibbs free energy models, activity coefficient equation can be derived (concept of partial molar property).

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Validity of Raoult's Law and Modified Raoult's Law

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Validity of Raoult's Law and Modified Raoult's Law

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Raoult's Law: VLE at low pressure and chemically similar species
Modified Raoult's Law: VLE at low pressure and chemically dissimilar species

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Activity coefficient of species in an Ideal gas mixture

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Activity coefficient of species in an Ideal gas mixture

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One.
Reason: There are no interactions in an ideal gas mixture (or) No like or unlike interactions of different magnitude.

Fact: Ideal gas mixture is a special case of ideal solution (magnitude of like and unlike interactions are equal and zero)

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Property of mixing: When to use mole numbers/fractions?

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Property of mixing: When to use mole numbers/fractions?

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When the system is defined extensively in terms of volume occupied/mole numbers/initial pressure include mole numbers in the evaluation of properties of mixing. In this case all the property relations should be written in terms of mole numbers

When the system is defined intensively in terms of mole fraction, evaluate properties of mixing on a per mole basis.

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For eg. I have a mixture containing 4 species (A,B,C,D). The activity coefficients calculated are positive for 3 of the species but negative for one of the species. For this case, will it be positive deviation or negative deviation? (or inconclusive?)

(Or will such a scenario never happen?)

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Ideal gas mixture model vs Ideal solution mixture model

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Ideal gas mixture model vs Ideal solution mixture model

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Is it correct to say that ideal gas mixture models apply to gas mixtures while ideal solution mixture model applies to liquid mixtures? I understand that you mentioned that "solution", "mixture", and "multi-component system" are used interchangeably in this course. But for the case of "ideal solution mixture model", does it mostly apply to liquid mixtures only?

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For this question, are we using ideal gas mixture model and also accounting for the deviation from the ideal gas mixture model by using the residual entropy values? so essentially, it's the calculation of the actual entropy of mixing, since the residual entropy values are given?

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How does all the equations the last column come about?

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Why is there no cap above the fi in xifi? is there any significance to that?

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Is gamma i (or natural log of gamma i?) and intensive property unique to each species in a real solution?

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is it correct to say that excess molar volume, excess molar enthalpy, excess molar entropy and excess molar gibbs energy are dependent on temperature, pressure, composition of species in real mixture and the nature of the chemical species? Also, I don't really understand what u mean by they are dependent on the nature of chemical species...

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How did you get the values for the ideal gas enthalphy of species 1 and 2? I can’t seem to get those numbers