Question

for a reaction, $delta h^0 = 206 kj/mol$ and $delta s^0 = 0.215 kj/(kcdot mol)$. at what temperatures is this reaction spontaneous?

a. at all temperatures
b. at temperatures greater than 958 k
c. at no temperature
d. at temperatures less than 44 k

Explanation:

Step1: Recall the Gibbs - free energy equation

The Gibbs - free energy change is given by $\Delta G=\Delta H - T\Delta S$, and a reaction is spontaneous when $\Delta G<0$.

Step2: Set up the inequality for spontaneity

We want $\Delta G<0$, so $\Delta H - T\Delta S<0$. Rearranging this inequality for $T$ gives $T>\frac{\Delta H}{\Delta S}$.

Step3: Substitute the given values

Given $\Delta H = 206\ kJ/mol$ and $\Delta S=0.215\ kJ/(K\cdot mol)$. Then $T>\frac{206\ kJ/mol}{0.215\ kJ/(K\cdot mol)}$.

Step4: Calculate the temperature

$\frac{206}{0.215}=958.14\ K$. So the reaction is spontaneous at temperatures greater than $958\ K$.

Answer:

B. At temperatures greater than 958 K