Question

The enthalpy of a reaction is 50 kj/mol, and the enthaply is 223 J/K mol. What is the minimum temperature for this reaction to be spontaneous?

Answer 1

for a reaction to be spontanous

dG < 0

and

dG = dH - T*dS

NOTE: you stated enthalpy for 223 J/K mol, but these are units of ENTROPY... also, we need entropy and will make much more sense that this is actually entropy, so I will assume it is entropy

so:

dG = dH - T*dS <0

so

50 kJ/mol - T * 233 J/mol * K <0

change all to J

50000 J/mol - T * 233 J/mol * K <0

solve for T

50000 < 233*T

T > 50000/233

T > 214.592 K

T must be at least slightly larger than 214.592 K in order to be spontanous