Entropy Change, ∆S (Oxford AQA International A Level Chemistry)

Entropy Change, ∆S

• In endothermic reactions the products are in a less stable, higher energy state than the reactants

  • So, why do endothermic reactions take place?

• The majority of chemical reactions we experience everyday are exothermic

• But,  ΔH^ꝋ alone is not enough to explain why endothermic reactions occur

Chaos in the universe

• The entropy (S) of a given system is the number of possible arrangements of the particles and their energy in a given system

  • In other words, it is a measure of how disordered or chaotic a system is

• When a system becomes more disordered, its entropy will increase

• An increase in entropy means that the system becomes energetically more stable

Entropy of a chemical reaction

• Using the thermal decomposition of calcium carbonate (CaCO₃) as an example:

CaCO₃ (s) → CaO (s) + CO₂ (g)

• In this reaction:

  • One reactant molecule forms two product molecules

    • Two molecules are more disordered than one

  • A solid molecule forms a solid molecule and a gas molecule

    • The gas molecule is more disordered than the solid reactant (CaCO₃), as it is constantly moving around

• As a result, the system has become more disordered and there is an increase in entropy

• Entropy changes for different chemical reactions are different because they depend on the number of reactants and products

Entropy of a state change

• Using the melting of ice to water as an example:

H₂O (s) → H₂O (l)

• In this example:

  • The water molecules in ice are in fixed positions and can only vibrate about those positions

    • They are not very disordered

  • The water molecules in liquid water are still quite close together but are arranged randomly and can move around each other

    • Therefore, water molecules in the liquid state are more disordered

• For any given substance, entropy increases when:

  • Its solid state melts into a liquid

  • Its liquid state boils into a gas

• For any given substance, entropy decreases when:

  • Its liquid state freezes into a solid

  • Its gaseous state condenses into a liquid

• For chemical reactions and state changes, the system with the higher entropy will be energetically favourable 

  • This is because the energy of the system is more spread out when it is in a disordered state

Feasible or spontaneous reactions

• Chemists talk about reactions being feasible or spontaneous

  • This means that reactions take place of their own accord

  • In other words, a reaction is energetically favourable

• This is an outcome of the second law of thermodynamics which broadly states the the entropy of the universe is always increasing

• We can see examples of this all around us:

  • Hot objects always cool and spread their heat into the surroundings, never the other way around

• Feasibility does not consider the rate of reaction

  • Feasibility states what is possible, not what actually happens

  • A feasible reaction might be incredibly slow, such as the rusting of iron

Calculating entropy changes

• Entropy changes are an order of magnitude smaller than enthalpy changes, so entropy is measured in joules rather than kilojoules.

  • The full unit for entropy is J K^-1 mol^-1

• The standard entropy change (ΔS) for a given reaction can be calculated using the standard entropies (S) of the reactants and products

• The equation to calculate the standard entropy change of a system is:

ΔS^ꝋ = ΣS_products^ꝋ - ΣS_reactants^ꝋ

• For example, the formation of ammonia from nitrogen and hydrogen:

N₂ (g) + 3H₂ (g) ⇋ 2NH₃ (g)

• The standard entropy change for this reaction is:

ΔS_system^ꝋ = (2 x ΔS^ꝋ(NH₃)) - (ΔS^ꝋ(N₂) + 3 x ΔS^ꝋ(H₂))

• NOTE: The standard entropies for each chemical in the reaction must be multiplied by its stoichiometric coefficient

• Unlike enthalpy of formation for elements, entropy for elements is not zero

  • Entropy values for elements and compounds are found in data books