Problem 41 - Chemistry and Chemical Reactivity

Question

Calculate the entropy change, \(\Delta S^{\circ}\), for the vaporization of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) at its normal boiling point, \(78.0^{\circ} \mathrm{C}\) The enthalpy of vaporization of ethanol is \(39.3 \mathrm{kJ} / \mathrm{mol}\).

Step-by-Step Solution

Answer

The entropy change for the vaporization of ethanol at its boiling point is approximately 111.9 J/mol K.

Step 1: Understand the problem

We need to calculate the entropy change, \(\Delta S^{\circ}\), for the vaporization of ethanol at its normal boiling point.

Step 2: Use the formula for entropy change

For a phase change at constant temperature, the formula used is \( \Delta S^{\circ} = \frac{\Delta H^{\circ}}{T} \), where \(\Delta H^{\circ}\) is the enthalpy of vaporization and \(T\) is the temperature in Kelvin.

Step 3: Convert Temperature to Kelvin

The boiling point of ethanol is given as \(78.0^{\circ} \mathrm{C}\). Convert this to Kelvin using the formula: \(T(K) = T(\degree C) + 273.15\). Therefore, \(78.0 + 273.15 = 351.15\, \mathrm{K}\).

Step 4: Plug values into the equation

Given \(\Delta H^{\circ} = 39.3\, \mathrm{kJ/mol}\), convert this to \(\mathrm{J/mol}\) to match units of entropy which are typically in Joules. Thus, \(\Delta H^{\circ} = 39300\, \mathrm{J/mol}\). Now substitute into \( \Delta S^{\circ} = \frac{39300}{351.15} \).

Step 5: Calculate the entropy change

Perform the division to find \(\Delta S^{\circ} = \frac{39300}{351.15} \approx 111.9\, \mathrm{J/mol\,K}\).

Key Concepts

Vaporization

Vaporization is the process where a liquid turns into a gas. This change occurs when molecules in a liquid gain enough energy to break free from the liquid's surface.
This can happen through two main processes: evaporation and boiling.

• Evaporation: Occurs at temperatures below the boiling point, typically at the surface of the liquid.
• Boiling: Occurs at a specific temperature called the boiling point, where the entire liquid can turn into gas.

Vaporization requires energy input to overcome intermolecular forces that hold the molecules together in the liquid phase. This energy is known as the enthalpy of vaporization.

Enthalpy

Enthalpy is a measure of the total energy in a thermodynamic system. For phase changes like vaporization, the enthalpy change describes the energy needed to transform a substance from one phase to another.
For ethanol, the enthalpy of vaporization is given as 39.3 kJ/mol. This value signifies the amount of energy required to convert one mole of liquid ethanol into vapor at constant pressure and temperature (its boiling point). To ensure proper unit conversions, remember:

• 1 kJ = 1000 J.

Ethanol

Ethanol, with the chemical formula \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), is a common alcohol used in beverages, antiseptics, and as a fuel. Its unique properties make it suitable for studying phase changes like vaporization.
When it vaporizes, ethanol goes from the liquid state to the gas state, requiring energy to break the hydrogen bonds between its molecules. Understanding its boiling point and enthalpy of vaporization is crucial in calculating the entropy change during this transition.

Boiling Point

The boiling point is the temperature at which a liquid's vapor pressure equals the external pressure, allowing it to turn into gas. It is a critical property in determining phase changes.
For ethanol, the normal boiling point is given as 78.0°C. To work with thermodynamic calculations, this temperature must be converted to Kelvin by adding 273.15, resulting in 351.15 K.
Calculating the boiling point in Kelvin is essential for formulas like \( \Delta S^{\circ} = \frac{\Delta H^{\circ}}{T} \), used to find the entropy change during vaporization at constant temperature.