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

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Answer 1 · 2018-05-09T07:26:39

$"T < 7528 K"$

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.](https://socratic.org/questions/what-is-delta-g)

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