To determine the Gibbs free energy change (ΔG) and the spontaneity of the phase change at 350 K, we need to use the Gibbs free energy equation:
[tex]\[ \Delta G = \Delta H - T \Delta S \][/tex]
where:
- [tex]\(\Delta H\)[/tex] is the enthalpy change, given as [tex]\(-44 \, \text{kJ/mol}\)[/tex]
- [tex]\(T\)[/tex] is the temperature, given as [tex]\(350 \, \text{K}\)[/tex]
- [tex]\(\Delta S\)[/tex] is the entropy change, given as [tex]\(-0.12 \, \text{kJ/(K \cdot mol)}\)[/tex]
Now, we will substitute these values into the Gibbs free energy equation:
[tex]\[ \Delta G = (-44) - (350 \times -0.12) \][/tex]
Next, we calculate the term [tex]\(350 \times -0.12\)[/tex]:
[tex]\[ 350 \times -0.12 = -42 \][/tex]
So, we have:
[tex]\[ \Delta G = -44 - (-42) \][/tex]
[tex]\[ \Delta G = -44 + 42 \][/tex]
[tex]\[ \Delta G = -2 \, \text{kJ/mol} \][/tex]
With [tex]\(\Delta G = -2 \, \text{kJ/mol}\)[/tex], we need to determine the spontaneity of the reaction. A negative [tex]\(\Delta G\)[/tex] indicates that the process is spontaneous.
Therefore, the values are:
- [tex]\(\Delta G = -2.0 \, \text{kJ}\)[/tex]
- The phase change is spontaneous.
Thus, the correct answer is:
C. [tex]\(\Delta G=-2.0 \, \text{kJ}\)[/tex]; spontaneous
