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Equilibrium Constant & Entropy (Edexcel International A Level Chemistry): Revision Note

Stewart Hird

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Equilibrium Constant & Entropy

  • The equation for calculating the total entropy change is:

ΔSꝋtotal = ΔS ꝋsys + ΔSꝋsurr

(sys = system and surr = surroundings) 

  • Remember that ΔSꝋtotal is positive for all spontaneous changes

  • There is very little change in ΔSꝋsys with a change in temperature unless there is a change in the state of one of the reactants or products

  • There will be a significant change in ΔSꝋsurr however

  • The entropy change of the surroundings during a chemical reaction is

entropy

  • Where ΔH is the enthalpy change and T is the absolute temperature (measured in kelvin)

  • We can use this information to determine whether a reaction is spontaneous at a given temperature

Worked Example

Is the decomposition of calcium carbonate into calcium oxide and carbon dioxide spontaneous at the given temperatures?

CaCO3(s) → CaO(s) + CO2(g)                ΔH = +177.9 kJ mol-1        ΔSsys = +160.4 J K-1 mol-1

  1. 293K (20 °C)

  2. 1173K (900 °C)

   Answer 1: at 293 K (20°C)

  • ΔSsurroundings = negative fraction numerator plus 177900 space straight J space mol to the power of negative 1 end exponent over denominator 293 space straight K end fraction = -607.2 J K-1 mol-1

  • ΔStotal(293K) = (+160.4 - 607.2) = -446.8 J K-1 mol-1

  • The decomposition of calcium carbonate is not spontaneous at 293K

   Answer 2: at 1173K (900°C)

  • ΔSsurroundings = negative fraction numerator plus 177900 space straight J space mol to the power of negative 1 end exponent over denominator 1173 end fraction= -151.7 J K-1 mol-1

  • ΔStotal(1173) = (+160.4 - 151.7) = +8.7 J K-1 mol-1

  • The decomposition of calcium carbonate is spontaneous when heated to 1173K

Relationship between entropy change and equilibrium constant

  • For a reversible reaction that can reach equilibrium, the equilibrium position can be reached from either side of the reaction

  • This means that both the forward and backward reactions are spontaneous

    • ΔS must be positive in both directions

  • For example, consider the following reaction:

N2O4 (g) ⇌ 2NO2 (g)

entropy-and-equilibria-graph

A graph of entropy against the percentage of NO2 in a mixture of N2O4 and NO2

  • The entropy of N2O4 is less than the entropy of the equilibrium mixture

  • The change in entropy from pure N2O4 to the equilibrium mixture is positive

    • The change is spontaneous

  • The entropy change for NO2 to the equilibrium mixture is also positive 

    • This change is also spontaneous

  • The entropy change for a mixture of the gases in any proportions moving towards the equilibrium position is also positive

  • Neither the forward nor backward reaction can go to completion as the entropy change from the equilibrium mixture to either the reactants or products is negative

  • At equilibrium, the total entropy change is zero

ΔStotal [forward reaction] = ΔStotal [backward reaction]

  • The relationship between the total entropy of the reaction and the equilibrium constant (Kc or Kp) is

ΔStotal = R lnK

Using total entropy change to calculate an equilibrium constant

  • Rearranging the equation mentioned above we get:

lnK = fraction numerator increment S subscript t o t a l end subscript over denominator R end fraction

  • Hence:

K = e to the power of fraction numerator increment S subscript t o t a l end subscript over denominator R end fraction end exponent

Relationship between equilibrium constant and equilibrium position

  • There is no hard rule for the relationship between equilibrium constant and the position of equilibrium 

  • As a general rule, we can say a very large value of K suggests the equilibrium position is pushed towards the products (right-hand side)

  • Similarly, a very small value of K suggests the equilibrium position is pushed towards the reactants (left-hand side)

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    Stewart Hird

    Author: Stewart Hird

    Expertise: Chemistry Lead

    Stewart has been an enthusiastic GCSE, IGCSE, A Level and IB teacher for more than 30 years in the UK as well as overseas, and has also been an examiner for IB and A Level. As a long-standing Head of Science, Stewart brings a wealth of experience to creating Topic Questions and revision materials for Save My Exams. Stewart specialises in Chemistry, but has also taught Physics and Environmental Systems and Societies.