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Titanium tetrachloride, commonly symbolized as \( \mathrm{TiCl}_{4} \), is a chemical compound in which one titanium atom is bonded to four chlorine atoms. This compound is often encountered in both industrial and chemical research settings.

This substance is interesting because it exists as a volatile liquid under normal conditions and has a relatively low melting point of \(-23.2^{\circ} \mathrm{C}\). It's also highly reactive with water, producing a dense white smoke of titanium dioxide and hydrochloric acid, making it an intriguing subject for chemical studies.

In thermodynamics, compounds like \( \mathrm{TiCl}_{4} \) provide valuable insights into phase changes, such as melting and boiling, offering practical examples for calculating thermal properties like entropy of fusion.

The enthalpy of fusion is a vital thermodynamic quantity that represents the heat required to change a substance from the solid phase to the liquid phase at constant pressure and temperature. For titanium tetrachloride, this value is noted as \( \Delta H_{\text{fusion}} = 9.37 \text{ kJ/mol} \).

This value indicates the amount of energy needed to overcome the lattice energy of the solid state of \( \mathrm{TiCl}_{4} \) so it can become a liquid. When solving problems involving phase changes, understanding and calculating the enthalpy of fusion allows us to delve into how energy is absorbed or released during the melting process.

By knowing \( \Delta H_{\text{fusion}} \), we can apply it in calculations to determine other properties, such as the entropy of fusion, illustrating the interconnected nature of thermodynamic variables.

Converting temperatures to the Kelvin scale is crucial in thermodynamic calculations, as Kelvin is the SI unit for temperature and is often used in scientific equations. The melting point for \( \mathrm{TiCl}_{4} \) is initially given in Celsius as \(-23.2^{\circ} \mathrm{C}\).

To convert this temperature to Kelvin, we use the formula \( T(K) = T(^{\circ}C) + 273.15 \).

By applying this conversion, \(-23.2 + 273.15 = 249.95 \text{ K}\). Accurate conversion is essential because using the Kelvin scale ensures that absolute temperature is considered during calculations, providing consistency and accuracy in determining thermodynamic properties like entropy.

Thermodynamics calculations involve understanding the relationships between various thermal properties during state changes. To determine the entropy of fusion, \( \Delta S_{\text{fusion}} \), for \( \mathrm{TiCl}_{4} \), we can use the equation:

• \( \Delta S_{\text{fusion}} = \frac{\Delta H_{\text{fusion}}}{T} \)

First, convert \( \Delta H_{\text{fusion}} \) from \( \text{kJ/mol} \) to \( \text{J/mol} \) by multiplying by 1000 (since 1 kJ = 1000 J). Thus, \( \Delta H_{\text{fusion}} = 9.37 \times 1000 = 9370 \text{ J/mol} \).

Substitute \( \Delta H_{\text{fusion}} = 9370 \text{ J/mol} \) and \( T = 249.95 \text{ K} \) into the formula:

• \( \Delta S_{\text{fusion}} = \frac{9370}{249.95} \approx 37.48 \text{ J/(K} \cdot \text{mol)} \)

These calculations highlight how thermodynamic principles apply to real-world substances, demonstrating the calculation of entropy changes and allowing deeper insights into material behaviors during phase changes.