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For a phase change, [tex]\(\Delta H^0 = -44 \, \text{kJ/mol}\)[/tex] and [tex]\(\Delta S^0 = -0.12 \, \text{kJ/(K·mol)}\)[/tex]. What are [tex]\(\Delta G\)[/tex] and the spontaneity of the phase change at [tex]\(350 \, \text{K}\)[/tex]?

A. [tex]\(\Delta G = -2.0 \, \text{kJ}\)[/tex]; nonspontaneous
B. [tex]\(\Delta G = -86 \, \text{kJ}\)[/tex]; spontaneous
C. [tex]\(\Delta G = -2.0 \, \text{kJ}\)[/tex]; spontaneous
D. [tex]\(\Delta G = -86 \, \text{kJ}\)[/tex]; nonspontaneous

Sagot :

GinnyAnswer
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
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