Question

question 15 of 30
for a phase change, $\triangle h^0 = 31$ kj/mol and $\triangle s^0 = 0.093$ kj/(k·mol). what are $\triangle g$ and the spontaneity of the phase change at 300 k?

a. $\triangle g = 59$ kj; nonspontaneous
b. $\triangle g = 3.1$ kj; spontaneous
c. $\triangle g = 3.1$ kj; nonspontaneous
d. $\triangle g = 59$ kj; spontaneous

Explanation:

Step1: Recall the Gibbs free energy formula

The formula for Gibbs free energy change (\(\Delta G^0\)) is \(\Delta G^0=\Delta H^0 - T\Delta S^0\), where \(\Delta H^0\) is the enthalpy change, \(T\) is the temperature in Kelvin, and \(\Delta S^0\) is the entropy change.

Step2: Substitute the given values

We are given \(\Delta H^0 = 31\space kJ/mol\), \(T = 300\space K\), and \(\Delta S^0=0.093\space kJ/(K\cdot mol)\). Substitute these values into the formula:
\(\Delta G^0=31\space kJ/mol-(300\space K\times0.093\space kJ/(K\cdot mol))\)
First, calculate \(300\times0.093 = 27.9\space kJ/mol\)
Then, \(\Delta G^0=31 - 27.9=3.1\space kJ/mol\)

Step3: Determine spontaneity

A reaction is spontaneous if \(\Delta G^0< 0\) and non - spontaneous if \(\Delta G^0>0\). Since \(\Delta G^0 = 3.1\space kJ/mol>0\), the reaction is non - spontaneous.

Answer:

C. \(\triangle G = 3.1\space kJ\); nonspontaneous