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10-cme_311_rxn_equilibria_3.pptxChemical Engineering Thermodynamics CME 311
Reactions Equilibria
Chapter 13
1
Reaction Equilibria in an Ideal Gas
Let’s define a new term: Standard Gibbs Energy Change of Reaction = ΔGᵒ(T)
This can be rearranged to the following…
Remember when we did standard heat of reactions in Chpt 4? This is a similar concept but for G
Standard Reference State
Standard state = Species in their natural form at 298 K and 1 atm
ΔGᵒf,298,i = standard G of formation of species i at 298 K
Analogous to ΔH from previous section
Data given in Table C.4
Standard Gibbs Example
Example: What is the standard G of formation for the following reaction?
Reaction Equilibria in an Ideal Gas
π is the product of species
Keq (T) = Dimensionless equilibrium constant of the reaction, as a function of T
Standard Gibbs/keq Example
Example: What is the keq for the following reaction at 298K?
Ideal Gas Reaction example:
The following ideal gas reaction occurs at 2 atm and 300 K.
If you initially have 100 mol A and 50 mol B with a keq of 0.05, what is the extent of reaction and conversion of A and B?
Ideal Gas Reaction Example
Example #2
For the following reaction, occurring at standard state, determine the keq
Reaction Efficiency
What can you do to increase the conversion of reactions and improve reaction efficiency?
Decrease the pressure
Remove the products as they are formed
System will continue to react in order to achieve equilibrium
Change your reaction temperature
Increase T if endothermic rxn (ΔHᵒ > 0)
Decrease T if exothermic rxn (ΔHᵒ < 0)
**This is the most common industrial answer
Modifying reaction temperature
How does temperature impact keq?
Why? Because ΔG298 can only be applied for systems at 298 K and ΔG varies with temperature
If you are curious, your book goes through this derivation in detail…
Procedure:
Find keq at 298 K = k1
Use above equation to solve for k2 … keq at modified temperature
Modified Rxn Temp: Example
Again, let’s consider the following reaction.
We previously determined that at 298 K and 1 atm the keq was 3.86 x 10-8
A) What would the new keq be if we raised the reaction temperature to 625 K?
B) If we started with 1 mole of C3H8, what would be the conversion?
Modified Rxn Temp: Example
Influence of Cp as a function of T
In this example, we assumed that Cp (ΔH) was independent of temperature
We previously discussed how both do vary with T (Chpt. 4)
What would happen if we repeat this example but take the temperature dependence into account?
We will not be doing this due to the complexity and length of this analysis
We would find:
ξ = 0.78 and X = 78%
Not much difference!
How do we know if we can neglect heat effects?
Determine Cp at both inlet and outlet conditions and see if there is much change
Reactions in Ideal liquid phase
A liquid phase is ideal when:
All the molecules are similar
All the molecules behave similarly
There are no unusual inter-molecule interactions
Examples of ideal liquids:
Hexane (C6H12) and Pentane (C5H10)
Methanol (CH4O) and Ethanol (C2H6O)
Reactions in ideal liquid phase
Superscript “id” = ideal solution
Where xi is the liquid mole fraction of i and HiL is the H of pure I in the liquid phase at T and P of the system
Similarly, it can be shown:
Chemical potential in i.d. liquid reactions
Recall:
Through application of the incompressible assumption and derivation we arrive at the following equation:
Reaction equilibria in ideal liquids
We showed earlier that:
Therefore, for an ideal solution:
After going through the same derivation as for an ideal gas:
Ideal Liquid Rxn Example:
The following reaction takes place at 350 K with a keq of 1.89.
If the reaction starts with 100 mol AA and 100 mol M, what is the extent of reaction? You may assume the liquid phase is ideal.
Ideal Liquid Rxn Example:
Non-Ideal Liquids
Introduce the term GE = Excess Gibbs energy
Excess
G
“Real”
G
Ideal
G
Activity Coefficient
Let’s define:
γ = Activity coefficient
Represents a measure of non-ideality for solutions
Due to the intermolecular interactions
If we have an ideal solution γ = 1
μ can be expressed as:
Leads to
Rxn. Equilibria for non-ideal solutions
We showed earlier that:
Going through rearrangement:
Reaction Equilibrium expression for Non-ideal solutions
How do we find γ?
For an ideal liquid, γ = 1
For a non-ideal liquid:
Several models for finding GE exist
You book goes through several techniques, starting on page 446
We are going to discuss one in particular – Margueles Equation
Margueles Equation
For a binary mixture:
Recall, γ can be expressed as….
Simultaneous solving of these 2 equations leads to:
Where A is a measure of interaction between the particles
While this is relatively straight-forward for a binary system, this rapidly gets complex for a multi-component system (n > 2).
Margueles Derivation
Let’s return to our previous example:
The following reaction takes place at 350 K with a keq of 1.89.
If the reaction starts with 100 mol AA and 100 mol M, what is the extent of reaction?
Now, assume that that is a non-ideal solution!
Included is the following table
| AA | M | MA | W | |
| ln γ | 7.8 | 3.3 | 9.8 | 2.1 |
Non-ideal liquid example
Non-Ideal Liquid Example
Given the following Rxn and expressions for the activity coefficients, T = 50 deg C, and an extent of reaction of 0.73, find keq. You start with 1 mole of A
Non-Ideal Liquid Example
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