Entropy of Vaporisation

Gibbs Free Energy Equilibrium: At the boiling point of a substance, the liquid and vapor phases exist in dynamic equilibrium. This state implies that the change in Gibbs free energy ($\\Delta G$) for the phase transition is exactly zero.

The Fundamental Equation: The relationship between enthalpy, entropy, and temperature is defined by the equation $\\Delta G = \\Delta H - T\\Delta S$. When $\\Delta G = 0$, the equation simplifies to $\\Delta H = T\\Delta S$, allowing one variable to be calculated if the others are known.

Temperature Dependency: The temperature ($T$) in these thermodynamic equations must always be expressed in Kelvin. For water, which boils at $100^{\circ}C$, the absolute temperature used in calculations is $373 K$.

Energy Quantification: To find the enthalpy of vaporisation, the total energy supplied to the system must be measured. This is achieved by using an electric heater (like a kettle) with a known power rating ($P$) and timing the duration ($t$) of boiling, where $Energy (Q) = P \\times t$.

Mass Loss Measurement: The amount of substance that has transitioned to the gas phase is determined by weighing the system before and after the boiling period. The difference in mass represents the mass of the liquid that evaporated.

Molar Conversion: The mass of the evaporated liquid is converted into moles ($n$) using the molar mass ($M_r$) of the substance. For water, the molar mass is approximately $18.0 g \\, mol^{-1}$.

Step-by-Step Calculation: First, calculate the enthalpy change per mole using $\\Delta H_{vap} = \\frac{Q}{n}$. Then, divide this enthalpy value by the boiling temperature in Kelvin to find the entropy change: $\\Delta S_{vap} = \\frac{\\Delta H_{vap}}{T}$.

Energy vs. Disorder: While enthalpy focuses on the 'cost' in terms of heat energy to break bonds, entropy focuses on the 'result' in terms of the increased freedom of the particles.

Scale of Units: It is critical to note that enthalpy is often calculated in kilojoules, whereas entropy is almost always reported in joules; a factor of $1000$ must be applied during calculations to ensure consistency.

Unit Consistency Check: Always verify that your enthalpy value is converted from $kJ$ to $J$ before dividing by temperature to get entropy. Failing to do this will result in an answer that is off by a factor of $1000$.

Kelvin Conversion: Ensure the boiling point is converted to Kelvin by adding $273$ to the Celsius value. Using Celsius in the denominator of the entropy formula is a frequent error that leads to incorrect results.

Power and Time: When calculating energy ($Q = P \\times t$), ensure the power is in Watts (Joules per second) and time is in seconds. If the power is given in $kW$, multiply by $1000$ first.

Sanity Check: For most simple liquids like water, the entropy of vaporisation is a significant positive value (often around $80-120 J K^{-1} mol^{-1}$). If your calculated value is extremely small or negative, re-examine your unit conversions.

Assuming $\Delta G$ is always zero: Students often forget that $\\Delta G = 0$ only applies at the specific temperature where the phases are in equilibrium (the boiling point). At other temperatures, the full Gibbs equation must be used.

Mass of the Kettle: In experimental setups, the mass of the container (kettle) is part of the total mass. However, only the change in mass matters for calculating the moles of substance evaporated.

Heat Loss to Surroundings: A common experimental error is assuming all energy from the heater goes into vaporising the liquid. In reality, some heat is lost to the air or used to heat the container itself, which can lead to an overestimation of $\\Delta H_{vap}$.