The decomposition of ammonium dichromate [(NH4)2Cr2O7] is called the volcano demonstration for its fiery display. The decomposition reaction involves breaking down ammonium dichromate into nitrogen gas, water vapor, and solid chromium(III) oxide. From the data in Appendix 4 and given kJ/mol and J/K mol for (NH4)2Cr2O7, calculate _G for the volcano reaction and calculate for ammonium dichromate.

ΔG° for the reaction = -2345.81 kJ

ΔG°f for Ammonium dichromate = 619.91 kJ

Explanation:

The decomposition of (NH₄)₂Cr₂O₇ is represented as

(NH₄)₂Cr₂O₇ (s) → N₂ (g) + 4H₂O (g) + Cr₂O₃ (s)

From literature, the standard enthalpy of formation (ΔH°f) of the products are given as

For N₂, 0 kJ/mol

For H₂O, -242 kJ/mol

For Cr₂O₃, -1128 kJ/mol

For (NH₄)₂Cr₂O₇, -23 kJ/mol (given in the question)

Also, their standard entropies are given as

For N₂, 192 J/mol.K

For H₂O, 189 J/mol.K

For Cr₂O₃, 81 J/mol.K

For (NH₄)₂Cr₂O₇, 114 J/mol.K (given in the question)

Note that the enthalpy of the reaction is given as

ΔH° = ΔH°(products) - ΔH°(reactants)

ΔH°(products) = (1×0) + (4×-242) + (1×-1128) = -2096 kJ

ΔH°(reactants) = (1×-23) = -23 kJ

ΔH° = -2096 - (-23) = -2073 kJ

Note that the entropy of the reaction is given as

ΔS° = ΔS°(products) - ΔS°(reactants)

ΔS°(products) = (1×192) + (4×189) + (1×81) = 1029 kJ/K

ΔS°(reactants) = (1×114) = 114 kJ/K

ΔS° = 1029 - (114) = 915 J/K = 0.915 kJ/K

The Gibb's free energy is then calculated thus

ΔG° = ΔH° - TΔS°

where T = absolute temperature in Kelvin at which the reaction takes place = 298.15K

ΔG° = -2073 - (298.15×0.915) = -2345.81 kJ

To calculate the ΔG°f for Ammonium dichromate, we need the ΔG°f for the products.

For N₂, 0 kJ/mol

For H₂O, -228.6 kJ/mol

For Cr₂O₃, -811.5 kJ/mol

For (NH₄)₂Cr₂O₇, let the standard free energy be x

ΔG° = ΔG°(products) - ΔG°(reactants)

ΔG°(products) = (1×0) + (4×-228.6) + (1×-811.5) = -1,725.9 kJ

ΔG°(reactants) = (1×x) = x kJ

ΔG° = -1,725.9 - (x)

Recall that ΔG° = -2345.81 kJ

-2345.81 = -1,725.9 - x

x = -1,725.9 + 2345.81 = 619.91 kJ

Hope this Helps!!!