Can I get help on this?

Question

Calculate Δ𝐺∘ at 298 K for the reaction CS2(l)+3O2(g)⟶CO2(g)+2SO2(g) based on these reactions. C(s)+O2(g)⟶CO2(g)Δ𝐺∘=−397.28 kJ/mol S(s)+O2(g)⟶SO2(g)Δ𝐺∘=−300.19 kJ/mol C(s)+2S(s)⟶CS2(l)Δ𝐺∘=+62.37 kJ/mol Δ𝐺∘= kJ/mol

Answer 1

I'm impressed with how @Amy B arrived at the correct answer. But I wanted to present an alternative way using Hess's Law.

Given

(1) C + O₂ ==> CO₂ .. ∆Gº = -397 kJ/mol

(2) S + O₂ ==> SO₂ .. ∆Gº = -300 kJ/mol

(3) C + 2S ==> CS₂ .. ∆Gº = 62 kJ/mol

Procedure

reverse eq (3): CS₂ ==> C + 2S .. ∆Gº = -62 kJ

copy eq(2) x 2: 2S + 2O₂ ==> 2SO₂ .. ∆Gº = 2 x -300 = -600 kJ

copy eq (1): C + O₂ ==> CO₂ .. ∆Gº = -397 kJ/mol

Add all together and combine/cancel like terms to get the equation of interest:

CS₂ + 2S + 2O₂ + C + O₂ ==> C + 2S + 2SO₂ + CO₂

CS₂ + 3O₂ ==> 2SO₂ + CO₂

∆Gº = -62 + -600 + -397 = -1059 kJ/mol

Answer 2

In this question, you are given the formation reactions for the relevant substances in your equation of interest, and you can calculate ∆G° by summing up the ∆G°s of formation for the reactants and products, accounting for their stoichiometric coefficients, and subtracting one from the other, according to this formula:

∆G°_rxn = Σn_products•∆G°_f(products) - Σn_reactants•∆G°_f(reactants)

∆G°_rxn = [1 mol CO₂ •∆G°_f(CO2) + 2 mol SO₂ •∆G°_f(SO2)] - [1 mol CS₂ •∆G°_f(CS2) + 3 mol O₂•∆G°_f(O2)]

= [(1 mol CO₂)(-397.28 kJ/mol CO₂) + (2 mol SO₂)(-300.19 kJ/mol SO₂)] - [(1 mol CS₂)(+62.37 kJ/mol CS₂) + (3 mol O₂)(0 kJ/mol O₂)]

= (-997.61 kJ) - (62.37 kJ)/ mol reaction

= -1,059.98 kJ/mol reaction

Note that the ∆G° of formation for O₂(g) is zero, since O₂(g) is the most stable elemental form of oxygen, and the formation reaction would be O₂(g) --> O₂(g), or NO REACTION