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Ch.9 - Thermochemistry: Chemical Energy
All textbooksMcMurry 8th EditionCh.9 - Thermochemistry: Chemical EnergyProblem 141
Chapter 9, Problem 141

What is the melting point of benzene in kelvin if ΔHfusion = 9.95 kJ/mol and ΔSfusion = 35.7 J/(K mol)?

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Identify the relationship between the melting point, enthalpy of fusion (\( \Delta H_{\text{fusion}} \)), and entropy of fusion (\( \Delta S_{\text{fusion}} \)). The melting point is the temperature at which the solid and liquid phases are in equilibrium, meaning \( \Delta G = 0 \).
Use the Gibbs free energy equation at equilibrium: \( \Delta G = \Delta H - T \Delta S = 0 \).
Rearrange the equation to solve for the temperature (melting point, \( T \)): \( T = \frac{\Delta H}{\Delta S} \).
Substitute the given values into the equation: \( \Delta H_{\text{fusion}} = 9.95 \text{ kJ/mol} \) and \( \Delta S_{\text{fusion}} = 35.7 \text{ J/(K mol)} \).
Convert \( \Delta H_{\text{fusion}} \) from kJ/mol to J/mol by multiplying by 1000, then calculate \( T \) using the rearranged equation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Phase Change and Melting Point

The melting point is the temperature at which a solid becomes a liquid at a given pressure. For substances like benzene, this is a critical phase transition point where the solid structure breaks down into a liquid state. Understanding the melting point is essential for predicting the behavior of substances under varying temperature conditions.
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Gibbs Free Energy and Phase Equilibrium

The Gibbs free energy change (ΔG) determines the spontaneity of a phase change. At equilibrium, ΔG is zero, which can be expressed using the equation ΔG = ΔH - TΔS. Here, ΔH is the enthalpy change and ΔS is the entropy change. This relationship is crucial for calculating the melting point using the provided enthalpy and entropy values.
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Thermodynamic Relationships

The relationship between enthalpy (ΔH), entropy (ΔS), and temperature (T) is fundamental in thermodynamics. The melting point can be calculated using the formula T = ΔH/ΔS, where ΔH is the heat absorbed during fusion and ΔS is the change in entropy. This equation allows us to find the temperature at which the solid and liquid phases coexist in equilibrium.
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Related Practice
Textbook Question
(d) What is the kinetic energy of an electron traveling at velocity (c)?
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Textbook Question

Ethyl alcohol has ΔHfusion = 5.02 kJ/mol and melts at - 114.1 °C. What is the value of ΔSfusion for ethyl alcohol?

Textbook Question
Metallic mercury is obtained by heating the mineral cinnabar (HgS) in air:HgS1s2 + O21g2 S Hg1l2 + SO21g2(a) Use the data in Appendix B to calculate ΔH° in kilojoules for the reaction.
Textbook Question

Methanol (CH3OH) is made industrially in two steps from CO and H2. It is so cheap to make that it is being considered for use as a precursor to hydrocarbon fuels, such as methane (CH4):

Step 1. CO(g) + 2 H2(g) → CH3OH(l) ΔS° = –332 J/K

Step 2. CH3OH(l) → CH4(g) + 1/2 O2(g) ΔS° = 162 J/K

(a) Calculate ΔH° in kilojoules for step 1.