The enthalpy of vaporisation of liquid diethyl ether \(-\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}\), is \(26.0 \mathrm{~kJ} \mathrm{~mol}^{-1}\) at its boiling point \(\left(35.0^{\circ} \mathrm{C}\right)\). Calculate \(\Delta S\) for conversion of : (a) liquid to vapour, and \(\quad\) (b) vapour to liquid at \(35^{\circ} \mathrm{C}\).

Understanding entropy change calculation is central when studying thermodynamics. Entropy, denoted as \( \Delta S \), is a measure of disorder or randomness within a system. During a phase transition, such as the vaporization of a liquid, the system's entropy changes.

Using the formula \( \Delta S = \frac{\Delta H_{vap}}{T} \), where \( \Delta H_{vap} \) is the enthalpy of vaporization and T is the temperature in Kelvin, you can calculate the change in entropy. It's important to note that this equation assumes a reversible process and that the temperature remains constant during the change of phase.\
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\In the case of liquid diethyl ether vaporizing, the positive value of \( \Delta S \) indicates an increase in entropy. This is due to the molecules in the vapor phase being much more disordered than in the liquid phase. Conversely, when a vapor condenses to a liquid, the entropy decreases, signifying a shift towards order, which is reflected by a negative entropy change.

Phase transitions are transformations between different states of matter: solids to liquids (melting), liquids to gases (vaporization), and vice versa for freezing and condensation. Each transition involves a change in energy, specifically the enthalpy of the substance, and a change in entropy, as the orderliness of the system's particles changes.

For instance, when diethyl ether vaporizes (liquid to gas), it requires energy which is absorbed from the surroundings, corresponding to the enthalpy of vaporization \( \Delta H_{vap} \). This process increases the distance between particles, resulting in more possible arrangements (states), and hence a higher entropy \( \Delta S \) of the system. Remember, every phase transition has an associated \( \Delta S \) value, and signifying the direction of the entropy change helps in predicting the nature of the process—whether it is endothermic or exothermic.

Temperature is a key variable in thermodynamic equations, and it's vital to use the absolute temperature scale, which is Kelvin (K), to ensure accuracy in calculations. The formula for converting Celsius to Kelvin is straightforward: \( T(K) = T(°C) + 273.15 \).

Why is this important? The Kelvin scale starts at absolute zero, the theoretical point where particles have minimum thermal motion, making it the natural choice in scientific research. This scale allows thermodynamic equations, like those used to calculate the entropy change for phase transitions, to work universally, without negative temperature values that would be nonsensical in those contexts.

For diethyl ether's boiling point at 35.0°C, converting to Kelvin gives us 308.15 K, which is then used in our entropy change calculation. This conversion forms the base for accurate and meaningful interpretations of thermal phenomena.