Chemistry

Chemistry

Problem

A 25.0 g25.0\,\text{g} sample of solid naphthalene (molar mass 128 g mol−1128\,\text{g mol}^{-1}) is initially at its melting point of 80.2 ∘C80.2\,^{\circ}\text{C}. In a closed, well-insulated vessel open to the atmosphere, the following sequence of events takes place: 1. The solid melts completely to liquid at 80.2 ∘C80.2\,^{\circ}\text{C}. 2. The liquid is then vaporized completely at its boiling point of 218 ∘C218\,^{\circ}\text{C}. 3. The hot vapor cools and condenses completely back to liquid at 218 ∘C218\,^{\circ}\text{C}. No temperature changes other than those listed occur, and pressure remains at 1 atm throughout. Molar enthalpies (at 1 atm): • ΔHfus=19.1 kJ mol−1\Delta H_\text{fus}=19.1\,\text{kJ mol}^{-1} • ΔHvap=41.4 kJ mol−1\Delta H_\text{vap}=41.4\,\text{kJ mol}^{-1} Answer the following questions about the overall energetic effect of the sequence. (a) Calculate the quantity of heat absorbed or released (include sign) during step 1. (b) Calculate the quantity of heat absorbed or released (include sign) during step 2. (c) Calculate the quantity of heat absorbed or released (include sign) during step 3. (d) Determine the net heat absorbed or released by the naphthalene sample for the entire sequence, and state whether the overall process is endothermic or exothermic. (e) Justify your answer in part (d) by discussing how the direction of energy flow in each individual step combines to produce the overall result.
Intuitive explanation

The key to this problem is recognizing that phase changes involve enthalpy transfers, and that a complete cycle returning to the same phase means you can track net energy flow. Calculate moles from the given mass, then sum the enthalpy changes for each step—melting absorbs heat, vaporization absorbs heat, and condensation releases that vaporization energy back. The overall ΔH\Delta H tells you whether the system gained or lost net energy through this sequence.

Intuitive explanation

The key to this problem is recognizing that phase changes involve enthalpy transfers, and that a complete cycle returning to the same phase means you can track net energy flow. Calculate moles from the given mass, then sum the enthalpy changes for each step—melting absorbs heat, vaporization absorbs heat, and condensation releases that vaporization energy back. The overall ΔH\Delta H tells you whether the system gained or lost net energy through this sequence.

Browse the problem library