Reaction Equilibria

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Reaction Equilibria

• Our ultimate goal is to be able to calculate how
  far a given reaction can proceed before
  equilibrium is reached.
• What is the equilibrium composition?
• Equilibrium does not mean the concentration of
  the reactants or products is equal. Rather, the
  rate at which reactants react to form products is
  the same as the rate at which products react to
  form reactants.
• http//www.wwnorton.com/chemistry/tutorials/ch15.h
  tm

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• Express all species in terms of the reaction
  coordinate.
• Calculate the equilibrium constant at the
  reaction temperature.
• Calculate the reaction coordinate.
• Calculate the equilibrium composition.

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1. Express all species in terms of the reaction
coordinate,
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Mole fraction
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If the feed contains twice as much moles of
oxygen as sulfur dioxide using air as a source of
oxygen, express the number of moles and the mole
fractions of all species in terms of the reaction
coordinate
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2. Calculate the equilibrium constant (K) at any
temperature.
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Application of Equilibrium Criteria to Chemical
Reaction
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Calculation of K To find we use available
thermochemical data
Example The direct conversion of methanol to
form hydrogen is considered as an attractive
method to generate hydrogen for fuel cells. The
reaction is carried at 600C and low pressure with
a feed of twice as much moles of water as
methanol. (a)    Calculate the mole fractions
of the species in the reaction (b)   How many
moles of hydrogen are produced per mole of
methanol if epsilon is 0.87
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• Express all species in terms of the reaction
  coordinate.
• Calculate the equilibrium constant at the
  reaction temperature.
• K stores the fugacity information
• K is constant only at a fixed temperature
• Calculating K at temperatures different from 298K
• Constant enthalpy
• Enthalpy f(T)
• Relation between K and composition (reactor
  conditions and the effect on K)
• Calculate the reaction coordinate.
• Calculate the equilibrium composition.

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This value would have been correct if the example
stated was at 250C. Instead the example says 600C
so we have to calculate the equilibrium constant
at a different temperature (ca. 600C).
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Temperature dependence of the equilibrium
constant, K
Case 1 Constant enthalpy of reaction
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Note the value of K increases by an order of
magnitude (4.69 vs. 37.44) as the temperature
increases from 250C to 600C. We should expect
this since the enthalpy of reaction is positive.
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Case 2 Enthalpy being a function of T
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Summary of the equilibrium constant, K
Effects of temperature, pressure, inerts and
non-stoichiometric reactants on chemical reactions
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• Example 3 We wish to produce formaldehyde by
  gas-phase pyrolysis of methanol in accordance to
  the following reaction
• (a)    What is the equilibrium constant at 298K?
  Would you expect any appreciable yield of
  product?
• (b)   Consider the reaction at 6000C and 1 bar.
  What is the equilibrium constant assuming
  constant enthalpy of reaction
• (c)    For the reaction at 6000C and 1 bar and
  enthalpy being a function of temperature,
  calculate the equilibrium constant.

Solution (a) equilibrium constant at 298K
Almost no product will be formed.
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Solution (b) equilibrium constant at 873K and
constant enthalpy
Some product will be formed.
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K
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Relation between equilibrium constants and
composition
So far we have learned how to calculate the
equilibrium constant, K at any temperature for a
given reaction. what we would like to do next is
calculate the equilibrium conversion and
composition.
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Effect of reactor conditions on the extent of
reaction
Temperature, pressure, inerts and
non-stoichiometric reactants
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The effect of Reactor Temperature We already saw
this
The effect of Reactor Pressure Restatement of
Le Chateliers principle
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The effect of inerts (species that dont take
part in reaction and dont have any retardation
effect)
If v gt 0 then increasing inerts increases
equilibrium conversion. The opposite is true for
V lt 0. If v 0 there is no inert effect.
Note Inters dont change the equilibrium
constant. Why?
The effect of non-stoichiometric reactants
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• Express all species in terms of the reaction
  coordinate.
• Calculate the equilibrium constant at the
  reaction temperature.
• K stores the fugacity information
• K is constant only at a fixed temperature
• Calculating K at temperatures different from 298K
• Constant enthalpy
• Enthalpy f(T)
• Relation between K and composition (reactor
  conditions and the effect on K)
• Calculate the reaction coordinate.
• Calculate the equilibrium composition.

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3. Calculate the reaction coordinate.
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• Example 5 The unimolecular decomposition of
  ethane to produce ethylene is shown.
• The reaction is carried at 1273K and 1 bar.
  Calculate the equilibrium composition assuming
  the enthalpy of reaction is constant.

Assumption ideal gas (1 bar)
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Equilibrium composition
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Example 6 Consider the production of Ammonia
from the catalytic reaction of stoichiometric
feed of nitrogen and hydrogen at 5000C and 1 bar.
What is the maximum conversion under the
assumption of (a) Constant enthalpy of
reaction (b) Enthalpy being a function of T
Assumption ideal gas
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Solution (a)
Solution (b)
http//www.mhhe.com/physsci/chemistry/essentialche
mistry/flash/flash.mhtml
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• Example 7 Repeat example 6 at 773K and 300 bar.
• If we assume ideal gas behavior

However at 300 bar we do not expect the gas to be
ideal and modification to account non-ideality is
essential.
When we use the Lewis fugacity rule we get
equilibrium conversion of 0.34 and if we use
cubic equation of state (vdW)for non-ideality we
get a value of 0.33.   Note Although conversion
drops by about 10 due to non-ideality of the
gas, the increase in pressure from 1 bar to 300
bar certainly increased the equilibrium
conversion.
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Case 2 Liquid-phase and solid-phase reactions
Example 8 Consider the isomerization of liquid
methylcyclopentane to liquid cyclohexane at 298K.
What is the equilibrium conversion? Take Gibbs
Energy of formation at 298 to be 31.7kJ/mol for
methylcyclopentane and 26.9kJ/mol for
cyclohexane. 
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Case 3 Heterogeneous Reaction

• There are important industrial reactions that
  involve two-phases.
• Roasting of ores
• Cement production etc.
• In these cases one solid is immiscible with the
  other solid causing multiple solid-phases to be
  in equilibrium.
• The free energies of the pure phases are
  functions of temperature only and independent of
  the amount of the other components in the
  mixture.
• Pressure has little effect on free energy and is
  neglected
• The above assumptions simplify our calculation
• Mole fraction is calculated from the given phase
  NOT from the total components involved in the
  reaction.

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Equilibrium constant for a heterogeneous reaction
Example 9 Consider a closed system where pure
calcium carbonate is at 1000K and in a vacuum.
Assuming that the two solids are immiscible at
the given temperature, calculate the pressure of
the system. The following data are available.
Lewis-Randall fugacity for our system equals the
pure solid fugacity and becomes unity. Thus K is
simply the partial pressure of carbon dioxide!
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Example 10 You have just ordered a cylinder of
acetylene but you are concerned that it might
react during shipment to form benzene. If the
initial pressure is 1 bar and the temperature is
298K. What is the equilibrium conversion and
corresponding final pressure in the system? The
reaction proceeds as follows.
This pressure corresponds to complete conversion
of acetylene. However benzene exerts a vapor
pressure in the cylinder at 298, we use Antoine
equation to get P 0.12bar. But we can still
ship acetylene. Why?
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Multiple Reaction Equilibria

• So far we have seen only single reactions
  (homogeneous and heterogeneous).
• However may industrial reactions are accompanied
  by competitive reactions other than the one we
  expect to happen.
• In this case each possible reaction will have its
  own reaction coordinate.
• Often solved using software packages although
  simpler ones can be computed in the old fashion
  way (manually).
• Equilibrium in electrochemical systems
  (fuel-cells) is also another aspect of reaction
  equilibria which we are not going to cover.

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Farwell, at least for now!