3.8 Entropy change for a chemical reaction

• entropy change accompanying a chemical reaction is defined as the difference between the sum of the entropies of all products and the sum of the entropies of all reactants.

• Thus for a reaction,

• The entropy change;

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• Where SM, SN, … are the entropies per mole of the various substances.

• If the reactants and products are in their standard states, then the entropy change becomes standard entropy change of reaction

• Where SoM, So

N …. refer to the standard molar entropies of the various substances.

• The entropy change of a reaction is generally evaluated at constant T an P

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• Entropy values of elements and compounds are calculated with the help of the 3rd Law of thermodynamics and values at 298K and 1atm are given, just like enthalpy values.

Example 3.1

• Calculate the standard entropy change for the reaction

<Cr2O3> + 3<C> = 2<Cr> + 3(CO) at 298K

Given: So

298<Cr2O3> = 81.17 J/K/mol

So298<C> = 5.69 J/K/mol

So298<Cr> = 23.76 J/K/mol

So298(CO) = 197.90 J/K/mol

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3.9 Variation of Entropy Change with Temperature

• If there is change of state of a system such that the temperature changes, the entropy change accompanying such a process can be calculated by integrating between the limit of the temperature

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• Where ST2 and ST1 are the entropies of the system at temperatures T2 and T1, respectively

• And since

• It follows that

• Or

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• The reference entropy is usually that at 298K, thus

• And for substances in their standard state, the expression becomes;

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• In the case of a chemical reaction involving reactants and products in their standard states, the changes in standard entropies and heat capacities must be considered

• Eqn 3.11 becomes

• If there is any phase transformation taking place between T1 and T2, then the entropy changes accompanying such transformations must be added

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• The eqn becomes;

Example 3.2

• Zinc melts at 420oC and its standard entropy at 25oC is 41.63 J/K/mol. Calculate the standard entropy of zinc at 750oC.

Given: ΔHfusion<Zn> = 7.28 kJ/mol

Cp<Zn> = 22.98 + 10.04 x 10-3 T J/K/mol

Cp[Zn] = 21.38 J/K/mol

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3.10 Entropy as Criterion for Equilibrium or Spontaneity

• The entropy function is useful in metallurgical operations in determining the direction in which a process will proceed and the final equilibrium state of the process.

• For a chemical reaction proceeding from initial state A to final state B, then

ΔStotal = ΔSB,total - ΔSA,total

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• In an isolated system of constant internal energy and constant volume,

oIf ΔStotal = 0, then the system is at equilibrium and no spontaneous change will occur

o If ΔStotal > 0, the reaction will occur spontaneously from sate A to state B

o If ΔStotal < 0, the reaction will occur spontaneously in the reverse direction i.e. from state B to state A

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• Thus for a chemical reaction within a system will have positive affinity to take place (or spontaneous) if it leads to an increase in entropy, without there being any exchange of heat with the surroundings.

• Most chemical reactions may be carried out either reversibly or irreversibly, but more heat is absorbed from the surroundings if the reaction is carried out in a reversible manner.

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