Gibb’s Free Energy – Ammonia

Calculate gibe's free energy - nitrogen + hydrogen to ammonia


In the question above, you are asked to calculate Gibb’s Free Energy for the Haber Process. The Haber Process is a process of manufacturing ammonia in a factory. The raw materials are nitrogen and hydrogen. Nitrogen is obtained by burning hydrogen in air. Hydrogen is obtained by reacting methane with steam. Haber Process combines nitrogen and hydrogen to create ammonia. Ammonia is used widely in household cleaners and other applications such as fertilizers, explosives and dyes.

TheHaberProcess - ammonia

Steps for calculating Gibb’s Free Energy

Remember:
amole

The equation N2 + 3H2 = 2NH3 tells you there are 3 moles of hydrogen and 2 moles of ammonia.

You will apply the moles to your calculations below.

  • 1. Sum up the entropies of reactants

  • The ΔTS are given in J/K•mol (joules per kelvin per mole). Multiply by the number of moles to obtain the total change in entropy.ΔTS (Nitrogen) + ΔTS (3 moles of Hydrogen) =
    192 + 3 x ( 131 ) = 585 J/K
  • 2. Calculate the entropy for ammonia

    ΔTS (2 moles of Ammonia) =
    2 x 193   = 386 J/K

  • 3. Calculate the entropy change of the whole process

    ΔTS (reactants) – ΔTS (product) =
    585 – 386 = -199 J/K

    • 4. Apply Gibb’s Equation

      ΔG = ΔH(system) – TΔS(system)

      = – 92 – (-0.199 x 298) = – 32.7 kJ

(nb. The value -0.199 kJK-1 mol-1 is the entropy per Kelvin temperature. You multiply it by 298 to get the entropy at 298 Kelvin temperature. )
(nb. the the TΔS is converted from joules to kilojoules)
(nb. ΔH is given in the question. You don’t need to work it out.)

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