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Entropy of vaporization is a crucial concept in thermodynamics, representing the degree of disorder or randomness introduced to a system when a liquid transforms into a vapor. In simpler terms, when a liquid substance, like mercury, changes to a gas, its particles move more freely, leading to increased disorder. This change in disorder is quantified as entropy change and is denoted as \( \Delta S_{vap} \).To illustrate, let's consider the step-by-step solution for mercury. The entropy of vaporization is given as \( 92.92 \mathrm{~J/K} \cdot \mathrm{mol} \). This value indicates that for every mole of mercury that vaporizes, there is a \( 92.92 \mathrm{~J/K} \cdot \mathrm{mol} \) increase in entropy. Understanding entropy allows us to predict the energy distribution in a system and how likely a process is to occur naturally. High entropy values often indicate a spontaneous process, as systems tend to move towards higher entropy states.

The Clausius-Clapeyron Equation is an essential tool for correlating pressures and temperatures in phase transitions, specifically between liquid and vapor states. This formula effectively predicts how the vapor pressure of a liquid changes with temperature. The equation is typically expressed as:\[ \frac{dP}{dT} = \frac{\Delta H_{vap}}{T \cdot \Delta V} \]However, in the context of boiling points, we can use a simplified version to calculate the boiling point of a liquid:\[ T_2 = \frac{\Delta H_{vap}}{\Delta S_{vap}} \]This simplification occurs because we consider a standard boiling point scenario, where pressure equals atmospheric pressure. By substituting mercury's enthalpy and entropy of vaporization into this equation, we find its normal boiling point. The significance of the Clausius-Clapeyron Equation lies in its ability to predict phase changes accurately, bridging thermodynamic properties such as enthalpy and entropy.

The normal boiling point of a substance is the temperature at which it changes from a liquid to a gas at standard atmospheric pressure. For mercury, determining this temperature requires understanding both its enthalpy and entropy of vaporization. In the provided solution, these values help calculate the exact boiling point using the Clausius-Clapeyron equation.In the calculation, we needed to find \( T_2 \), the boiling point of mercury, by using:\[ T_2 = \frac{58510 \mathrm{~J/mol}}{92.92 \mathrm{~J/K \cdot mol}} \]The outcome is \( 629.44 \mathrm{~K} \), which is the normal boiling point of mercury at 1 atmosphere pressure. Knowing this temperature is crucial for practical applications, as mercury's unique properties make it an important element in various fields, especially in thermometry and scientific research.