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Consider a substance that undergoes a phase transition from a solid to a liquid at its melting point. The melting point of the substance is $\mathrm{100^{\circ}C}$ . The molar enthalpy of fusion $\mathrm{\left(\Delta H_{\text {fusion }}\right)}$ is 10 kJ/mol, and the molar entropy of fusion $\mathrm{\left(\Delta S_{\text {fusion }}\right)}$ is 30 J/(mol K).Calculate the change in Gibbs free energy $\mathrm{(\Delta G)}$ for the phase transition at its melting point.
Option: 1
- 1194.5 J/mol not favoured phase transition

Option: 2
- 2000 J/mol

Option: 3
- 1194.5 J/mol favoured phase transition

Option: 4
-3993 J/mol

Answers (1)

best_answer

The change in Gibbs free energy $\mathrm{(\Delta G)}$ for a phase transition is given by the equation:

$\mathrm{\Delta G=\Delta H-T \Delta S}$

Where:
• $\mathrm{\Delta G}$ is the change in Gibbs free energy.
• $\mathrm{\Delta H}$ is the change in enthalpy.
• T is the temperature in Kelvin (K).
• $\mathrm{\Delta S}$ is the change in entropy.
We are given:

$\\\mathrm{\Delta H_{\text {fusion }}=10 \mathrm{~kJ} / \mathrm{mol}(convert to J / \mathrm{mol}: 10 \times 1000 \mathrm{~J} / \mathrm{mol})}\\ \\\mathrm{\Delta S_{\text {fusion }}=30 \mathrm{~J} /(\mathrm{mol} \mathrm{K})}\\ \\\mathrm{- Temperature (T)=100^{\circ} \mathrm{C}=373.15 \mathrm{~K} (melting \; point \; in \; Kelvin)}$

Now, let’s plug in the values and calculate $\mathrm{\Delta G}$ :

$\mathrm{\begin{aligned} & \mathrm{\Delta G}=(10,000 \mathrm{~J} / \mathrm{mol})-(373.15 \mathrm{~K} \times 30 \mathrm{~J} /(\mathrm{mol} \mathrm{K})) \\ & =-1,194.5 \mathrm{~J} / \mathrm{mol} \end{aligned}}$

The change in Gibbs free energy $\mathrm{(\Delta G)}$ for the phase transition from solid to liquid at the substance’s melting point is approximately −1,194.5 J/mol. This negative value indicates that the phase transition is favored at the given temperature, which is consistent with substances typically melting at their melting points under standard conditions.
So, the correct option is 3

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