Naphthalene, better known as 'mothballs,' has bp = 218 °C and ΔH_vap = 43.3 kJ>mol. What is the entropy of vaporization, ΔS_vap in J/(K mol) for naphthalene?

Verified step by step guidance

1. Identify the given values: boiling point (T) = 218 °C, which needs to be converted to Kelvin by adding 273.15, and the enthalpy of vaporization (ΔH_vap) = 43.3 kJ/mol, which needs to be converted to Joules by multiplying by 1000.
2. Convert the boiling point from Celsius to Kelvin: T(K) = 218 °C + 273.15.
3. Convert the enthalpy of vaporization from kJ/mol to J/mol: ΔH_vap(J/mol) = 43.3 kJ/mol × 1000 J/kJ.
4. Use the thermodynamic equation for entropy of vaporization: ΔS_vap = ΔH_vap / T.
5. Substitute the values of ΔH_vap and T into the equation to calculate ΔS_vap.

Key Concepts

Entropy of Vaporization (ΔS_vap)

The entropy of vaporization is a thermodynamic quantity that measures the change in entropy when a substance transitions from a liquid to a vapor. It reflects the degree of disorder in the system; a higher ΔS_vap indicates greater disorder in the gaseous state compared to the liquid state. This concept is crucial for understanding how temperature and energy changes affect phase transitions.

Gibbs Free Energy and Phase Changes

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the direction of chemical reactions and phase changes. The relationship between Gibbs Free Energy, enthalpy (ΔH), and entropy (ΔS) is given by the equation ΔG = ΔH - TΔS. For a phase change at equilibrium, ΔG is zero, allowing us to relate ΔH and ΔS to calculate the entropy of vaporization.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation describes the relationship between the vapor pressure of a substance and its temperature, providing a way to calculate the entropy of vaporization. It states that the slope of the vapor pressure curve is proportional to the enthalpy of vaporization divided by the temperature. This equation is essential for understanding how changes in temperature affect the vaporization process and the associated entropy changes.