Question

The molar heat of vaporization of ethanol is \(39.3 \mathrm{~kJ} / \mathrm{mol}\) and the boiling point of ethanol is \(78.3^{\circ} \mathrm{C}\) Calculate \(\Delta S\) for the vaporization of \(0.50 \mathrm{~mol}\) ethanol.

Short answer

The entropy change for the vaporization of 0.50 mol ethanol is 111.82 J/mol.K.

Step-by-step solution

Convert temperature to Kelvin

To convert °C to Kelvin, you add 273.15 to the °C value. For us, this means \(T = 78.3°C + 273.15 = 351.45K\).

Convert heat of vaporization to J/mol

Given value of heat of vaporization is in kJ/mol. To do calculations correctly, we need to make sure all the units match. To convert kJ to J, multiply the kJ value by 1000. Thus, \(\Delta H_vap = 39.3 kJ/mol × 1000 = 39300 J/mol\).

Calculate entropy change using the formula

Now we can substitute the values into the formula \(ΔS = \(\frac{q_{rev}}{T}\)\). This gives: \(\Delta S = \(\frac{39300 J/mol}{351.45K}\) = 111.82 J/mol.K\).

Key concepts

Molar Heat of Vaporization

The molar heat of vaporization is the amount of energy needed to convert one mole of a liquid into vapor without changing its temperature. For ethanol, this value is given as \(39.3 \text{ kJ/mol}\). This means that every mole of liquid ethanol requires 39.3 kilojoules of energy to become vapor. Understanding this concept is essential for calculating changes in entropy during phase transitions, as it directly links the energy required to the process of vaporization.

Boiling Point

The boiling point of a substance is the temperature at which its vapor pressure equals the atmospheric pressure. For ethanol, the specified boiling point is \(78.3^{\circ} \text{C}\). At this temperature, ethanol can transition from liquid to gas. Knowing the boiling point is important because it sets the stage for calculations involving temperature and energy changes, such as when using entropy formulas.

Temperature Conversion

Temperature conversion is crucial when dealing with scientific calculations, particularly those involving thermal dynamics. In the exercise, the Celsius temperature was converted to Kelvin. To convert from Celsius to Kelvin, simply add 273.15 to the Celsius temperature. For ethanol's boiling point of \(78.3^{\circ} \text{C}\), the conversion to Kelvin results in \(T = 78.3 + 273.15 = 351.45 \text{ K}\). Kelvin is used because it is the SI unit for thermodynamic temperature, which is necessary for accurate scientific work.

Thermal Calculations

Thermal calculations often involve specific formulas, such as the one for entropy change: \(\Delta S = \frac{q_{\text{rev}}}{T}\). Here, \(q_{\text{rev}}\) represents the heat absorbed or released, and \(T\) stands for temperature in Kelvin. In this exercise, the heat of vaporization \( (39.3 \text{ kJ/mol})\) is converted into joules \((39300 \text{ J/mol})\) for calculation consistency. The entropy change for the vaporization of 0.50 mol of ethanol is then calculated using these values, delivering a final result of \(111.82 \text{ J/mol.K}\). These calculations allow us to understand energy dispersal during phase shifts.