Delta H is 20.1 kJ/mol and Delta S is 45.9 J/(mol-k). Assuming these values change very little with temperature, over what temperature range is the reaction spontaneous in the forward direction?

Question

Is the reaction spontaneous for temperatures less than or greater than the solved temperature?

here's what i did but i doubt it's correct
-0.0001 = ∆H -T∆S
-0.0001 = (20.1 kJ/mol) - T(45.9 J/mol-k)
-20.1001 = -45.9T
the reaction is spontaneous for temperatures greater than T = 0.4379 K?

i used -0.0001 to make Delta G spontaneous

Answer 1

Right ball park but out at first base.
One USUALLY sets dG = 0 although your -0.0001 is not right ONLY for those values between zero and -0.0001 (of course the mathematicians probably will say that's an infinite number of dG values). Next, and a much larger error is you mixed units. DH is given in kJ/mol and dS in J/mol. You need to change one of them. Therefore, your T value is too small by a factor of 1000. It should be 437.9 K.

Answer 2

Dang.. thanks DrBob!