Gibbs Free Energy Worksheet - Answer Key

 

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  1. What is Gibb’s free energy? What is its symbol?

    This value represents the maximum amount of useful work (non PV-work) that can be obtained by a system.

    It is symbolized by G.  We only really discuss changes in free energy so you will normally deal with ΔG.

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  2. What is the equation for Gibbs Free Energy (ΔG)?

    ΔG = ΔH - TΔS

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  3. Why is it such a useful state function?

    It can be used to indicate the direction of spontaneity of a reaction, based only on values of the system. 

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  4. What sign must ΔG have to indicate a spontaneous process?

    ∆G must be negative.

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  5. At what temperatures would the following processes be spontaneous?

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    • +ΔS, -ΔH

      Spontaneous at all temperatures.

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    • -ΔS, -ΔH

      Spontaneous at sufficiently low temperatures.

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    • +ΔS, +ΔH

      Spontaneous at sufficiently high temperatures.

    • -ΔS, +ΔH

      Not spontaneous in the forward direction.

     

     

  6. For
    2NO2(g)     N2O4(g)

    • ΔH° is -58.03 kJ and ΔS° is -176.6J/K.  What is the value of ΔG° at 298K?

      ΔGo = –5403 J

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    • At what temperature is ΔG° = 0 (assume ΔH° and ΔS° are not temp. dependent).

      T = 328.6 K  

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    • Would ΔG° be negative above or below that temp?

      ∆Go would be negative at temperatures below 328.6K. 

     

     

  7. For the following constant pressure process

    2O(g)    → O2(g)

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    • Sign of ΔH?

      Negative.

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    • Sign of ΔS?

      Negative.

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    • Would this process be spontaneous at low or high temperatures?

      Spontaneous at sufficiently low temperatures. 

     

     

  8. ΔGo gives us important information about the equilibrium position of a reaction.

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  9. The value of ΔG depends on the concentration and pressure of reactants and products.  Therefore the value of ΔG changes as a reaction proceeds.

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  10. At equilibrium the value for ΔG is zero.

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  11. Provide an equation for the following relationships:

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    • ΔG (non-standard) to concentrations/pressures of reactants/products.

      ΔG = ΔGo + RT ln (Q)

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      • When would you use this equation?

        When you need to solve for the free energy for a system not under standard conditions.

       

    • Relates ΔG° to K

      ΔGo = –RT ln (K)

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      • When would you use this equation?

        When solving for the standard free energy of a system or for the equilibrium constant given the standard free energy.
    • Relates K to T

      ln K = (ΔHo/R) (1/T)  +  (ΔSo/R)

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      • What is important about the format of this equation?

        It is written in y = mx + b format – the equation of a line. 
    • Van’t Hoff Equation

      ln (K2/K1) = (–ΔHo/R)(1/T2  – 1/T1)

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      • When would you use this equation?

        To calculate K at any temperature for a reaction if you know K  at another temperature.

     

     

  12. Consider

    4NH3(g) + 5O2(g) 4NO (g) + 6H2O(g)

    Calculate K at 825°C if ΔH° is -908kJ and ΔS° is 181J/K

    K = 4.49 x 1052

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  13. What is free energy of formation?

    The free energy of formation is the amount of energy required to form a molecule from its elements in their standard states.

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  14. What is the symbol for the free energy of formation?

    (ΔGfo)

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  15. What is the free energy of formation for an element in its standard state?

    Zero. It would not require any energy to get an element in its standard state.

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  16. What is the equation used to solve for the free energy of reaction using the free energy of formation?

    ∆Gorxn = ∑∆Gof (product) -  ∑∆Gof (reactant)

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