The factor of  $\Delta G$ values is important in metallurgy.  The $\Delta G$  values for the following reactions at ${800}^{0}C$  are given as follows.
$S_2\left(s\right)+2O_2\left(g\right)\to 2S{O}_2\left(g\right):\Delta G=-544kJ$
$2Zn\left(s\right)+S_2\left(s\right)\to 2ZnS\left(s\right):\Delta G=-293kJ$
$2Zn\left(s\right)+O_2\left(g\right)\to 2ZnO\left(s\right):\Delta G=-480kJ$
The $\Delta G$ for the reaction $2ZnS\left(s\right)+3O_2\left(g\right)\to 2ZnO\left(s\right)+2S{O}_2\left(g\right)$  will be  $\left(kJ\right)$

Calculation of ΔG for Reaction in Metallurgy

The question involves determining the ΔG value (Gibbs free energy change) for the reaction: 
2ZnS(s) + 3O₂(g) → 2ZnO(s) + 2SO₂(g)
using the given ΔG values for related reactions. The ΔG value is an important factor in metallurgy as it determines the feasibility of a reaction.

Concept: To calculate the ΔG value of a reaction, we use the principle of Hess's Law, which states that the total ΔG for a reaction can be calculated by adding or subtracting the ΔG values of individual reactions that combine to give the overall reaction. The given reactions and their ΔG values are: 
Reaction 1: S₂(s) + 2O₂(g) → 2SO₂(g); ΔG = -544 kJ
Reaction 2: 2Zn(s) + S₂(s) → 2ZnS(s); ΔG = -293 kJ
Reaction 3: 2Zn(s) + O₂(g) → 2ZnO(s); ΔG = -480 kJ

Steps to Calculate ΔG:

1. The target reaction is: 
   2ZnS(s) + 3O₂(g) → 2ZnO(s) + 2SO₂(g).
2. We combine the given reactions to form the target reaction:
   • From Reaction 1, we get 2SO₂(g). This is used directly, so: 
     ΔG₁ = -544 kJ.
   • From Reaction 2, 2ZnS(s) is formed, but we need to reverse this reaction to use 2ZnS(s) as a reactant: 
     Reversing Reaction 2 gives: 
     2ZnS(s) → 2Zn(s) + S₂(s); ΔG = +293 kJ.
   • From Reaction 3, 2Zn(s) reacts with O₂(g) to form 2ZnO(s). This is used directly, so: 
     ΔG₃ = -480 kJ.
3. Add up the ΔG values to get the total ΔG for the target reaction: 
   ΔG = ΔG₁ + ΔG₃ - ΔG₂.
4. Substituting the values: 
   ΔG = (-544) + (-480) + (+293) = -731 kJ.

Final Answer: The ΔG for the reaction 2ZnS(s) + 3O₂(g) → 2ZnO(s) + 2SO₂(g) is -731 kJ.