Question

`CO (s) + S (s) + 2O_2 (g) -> CaSO_4 (s)` `DeltaH_(rxn)^@ = -888.3 " kJ/mol", DeltaS_(rxn)^@ = -118.0 "J/mol K"` At what temperature will this reaction be spontaneous?

Answer 1

`"T < 7528 K"`

Explanation:

At standard conditions

`"ΔG"^@ = Δ"H"^@ - "T"Δ"S"^@`

`"ΔG"^@ < 0` - Reaction is spontaneous
`"ΔG"^@ = 0` - Reaction is at equilibrium
`"ΔG"^@ > 0` - Reaction is non-spontaneous

For reaction to be at equilibrium

`0 = Δ"H"^@ - "T"Δ"S"^@`

`"T" = (Δ"H"^@)/(Δ"S"^@) = (-888.3 × 10^3\ "J/mol")/(-118.0\ "J/mol K") ≈ "7528 K"`

∴ Reaction is spontaneous at any temperature below `"7528 K"`

For more explanation on `"ΔG"` click here.