Energy Balances with Reaction

1
Energy Balances with Reaction

• In any chemical reaction, energy is required to
  break the reactant bonds and energy is released
  when the product bonds are formed
• The large changes in enthalpy and internal energy
  during a chemical reaction necessitates
  substantial heat transfer (heating or cooling)
  from the reactor in order to maintain the reactor
  at its desired operating temperature
• The net change of enthalpy is called the heat of
  reaction, and is the energy that must either be
  transferred to or from the reactor to maintain
  the desired reactor temperature

2
Heats of Reaction

• By definition, the heat of reaction, ?Hr (T,P),
  is the enthalpy change for a process in which
  stoichiometric quantities of reactants at
  temperature T and pressure P react completely to
  form products at the same temperature and
  pressure.
• For the following reaction,
• ?Hr is calculated as the difference between the
  product and reactant enthalpies (at constant T,P)
  which are weighted by their stoichiometric
  coefficients. Therefore,

3
Heats of Reaction

• The units of ?Hr are kJ/mol but, per mole of
  what?? Recall that the reported ?Hr applies to
  stoichiometric quantities of each species. For
  example,
• 2A B ? 3C ?Hr (100?C, 1 atm) -50 kJ/mol
• the enthalpy change for the given reaction is
• If 150 mol of C/s was generated at 100?C and 1
  atm,

4
Heats of Reaction Extent of Reaction

• In general, if nA,r moles of A are generated or
  consumed by reaction at a temperature T and
  pressure P and ?A is the stoichiometric
  coefficient of the reactant or product, the
  associated enthalpy change is
• Recall that the extent of reaction, ?, is a
  measure of how far a reaction has proceeded.

5
Notes on Heats of Reaction

• If ?Hr (T,P) is negative, the reaction is
  exothermic energy must be removed from the
  reactor to keep the temperature from increasing
• If ?Hr (T,P) is positive, the reaction is
  endothermic energy must be added to the reactor
  to keep the temperature from decreasing
• At low and moderate pressure, ?Hr (T,P) is nearly
  independent of pressure. Therefore, ?Hr (T,P) ?
  ?Hr (T)
• The value of the heat of reaction depends on how
  the stoichiometric equation is written. For
  example
• CH4(g) 2 O2(g) ? CO2(g) 2 H2O(l)
  ?Hr1 (25?C) -890.3 kJ/mol
• 2 CH4(g) 4 O2(g) ? 2 CO2(g) 4 H2O(l) ?Hr2
  (25?C) -1780.6 kJ/mol

6
Notes on Heats of Reaction

• The value of the heat of reaction depends on the
  phase of the reactants and products. For
  example
• CH4(g) 2 O2(g) ? CO2(g) 2 H2O(l) ?Hr1
  (25?C) -890.3 kJ/mol
• CH4(g) 2 O2(g) ? CO2(g) 2 H2O(g) ?Hr2
  (25?C) -802.3 kJ/mol
• The standard heat of reaction, ?Hr?, is the heat
  of reaction when both reactants and products are
  at standard conditions, 25?C and 1 atm.

The symbol ? denotes standard conditions (i.e.,
25?C and 1 atm).
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Example

• The standard heat of the combustion on n-butane
  vapour is
• Calculate the rate of enthalpy change,
  if 2400 mol/s of CO2 is produced in this
  reaction and the reactants and products are all
  at 25?C.
• What is the standard heat of the reaction
• 2 C4H10(g) 13 O2(g) ? 8 CO2(g) 10 H2O(l)
• Calculate if 2400 mol/s of CO2 is produced
  in this reaction and the reactants and the
  products are all at 25?C.

8
Example

• The heats of vapourization of n-butane and water
  at 25?C are 19.2 kJ/mol and 44.0 kJ/mol,
  respectively. What is the standard heat of the
  reaction
• Calculate if 2400 mol/s of CO2 is produced
  in this reaction and the reactants and products
  are all at 25?C.

9
Closed System Reactions

• What if the reaction takes place in a closed
  system of constant volume?
• Energy balance ?U ?Ek ?Ep Q W
• The internal energy of reaction, ?Ûr (T), is
  calculated as the difference between the product
  and reactant internal energies if stoichiometric
  quantities of reactants react completely at
  temperature T.
• Assuming ideal gas behaviour, the internal energy
  is related to the heat of reaction by
• where ?I is the stoichiometric coefficient of the
  ith gaseous reactant or product.

10
Example

• The standard heat of the reaction
• C2H4(g) 2 Cl2(g) ? C2HCl3(l) H2(g) HCl(g)
• is ?Hr? -420.8 kJ/mol. Calculate ?Ûr? for this
  reaction.