#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.