Problem 30 - Chemical Principles: The Quest for Insight

Question

(a) At its boiling point, the vaporization of \(0.235 \mathrm{~mol} \mathrm{CH}_{4}(1)\) requires \(1.93 \mathrm{~kJ}\) of heat. What is the enthalpy of vaporization of methane? (b) An electric heater was immersed in a flask of boiling crhanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), and \(22.45 \mathrm{~g}\) of ethanol was vaporized when \(21.2 \mathrm{~kJ}\) of energy was supplied. What is the enthalpy of vaporization of ethanol?

Step-by-Step Solution

Answer

\( \Delta H_{vap} \) of methane is \(8.21 \, \mathrm{kJ/mol}\); \( \Delta H_{vap} \) of ethanol is \(41.36 \, \mathrm{kJ/mol}\).

Step 1: Calculate the enthalpy of vaporization of methane

Use the formula for enthalpy change, \( \Delta H = \frac{q}{n} \), where \( q \) is the heat supplied in kilojoules, and \( n \) is the amount of substance in moles. Given \( q = 1.93 \, \mathrm{kJ} \) and \( n = 0.235 \, \mathrm{mol} \), plug the values into the formula to calculate the enthalpy of vaporization for methane.

Step 2: Calculate the enthalpy of vaporization of ethanol

Start with the same formula, \( \Delta H = \frac{q}{n} \). First, calculate the number of moles of ethanol vaporized using its molar mass. Ethanol (\( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \)) has a molar mass of approximately \( 46.07 \, \mathrm{g/mol} \). Then, use the given heat energy \( q = 21.2 \, \mathrm{kJ} \) to find the enthalpy of vaporization for ethanol.

Step 3: Determine the number of moles of ethanol

Calculate the moles of ethanol by using the formula \( n = \frac{m}{M} \), where \( m \) is the mass in grams and \( M \) is the molar mass. For ethanol, \( m = 22.45 \, \mathrm{g} \) and \( M = 46.07 \, \mathrm{g/mol} \).

Step 4: Compute the enthalpy of vaporization for ethanol

After obtaining the number of moles of ethanol from the previous step, use the enthalpy change formula \( \Delta H = \frac{q}{n} \) to calculate the enthalpy of vaporization for ethanol using the number of moles and the given heat energy.

Key Concepts

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the relationship between chemical reactions and energy changes involving heat. Understanding thermochemistry is crucial for deciphering how much energy is absorbed or released during a chemical process. In essence, it's the study of the heat changes that accompany chemical reactions and phase changes.

Heat, measured in joules or kilojoules, is a form of energy. When substances undergo a chemical or physical change, they absorb or release this energy mostly in the form of heat. The amount of heat transferred can tell us a lot about the process at hand, for example, whether a reaction is endothermic (absorbs heat) or exothermic (releases heat). The enthalpy of vaporization is one specific type of heat change, representing the energy required to change a liquid into a gas at its boiling point under standard conditions.

Enthalpy Change Calculations

Enthalpy change, symbolized by \( \Delta H \), represents the heat absorbed or released during a reaction occurring at constant pressure. It's an important concept in calculating energy changes in thermochemical equations. The enthalpy of vaporization is a specific type of enthalpy change that refers to the energy required to convert a liquid into a vapor.

To calculate the enthalpy change for a phase transition, like vaporization, you would use the formula:\[ \Delta H = \frac{q}{n} \], where \( q \) is the heat absorbed or released in kilojoules and \( n \) is the number of moles of substance undergoing the phase change. By understanding how to manipulate this equation, students can determine the thermal energy involved in vaporizing a certain amount of a liquid substance.

Phase Change Energy

Phase change energy is the amount of energy required to change a substance from one state to another without changing the temperature. For example, boiling, melting, freezing, and condensing, all require a transfer of energy. The amount of energy involved depends on the substance and the phase change it's undergoing.

The enthalpy of vaporization is the energy required for the phase change from liquid to gas at a constant temperature. This is a critical value for understanding how much energy is required to vaporize a liquid at its boiling point. Every substance has a unique enthalpy of vaporization, which can be used to calculate the energy requirements for processes such as distillation or the production of steam.

Molar Mass

Molar mass, which has units of grams per mole (g/mol), is the mass of one mole of a substance. It is an intrinsic property of each substance, determined by the combined atomic masses of all the atoms in a molecule. For compounds, you sum the atomic masses of each constituent element according to its stoichiometry in the compound. Molar mass allows us to convert between the mass of a substance and the number of moles, providing a critical link in calculating the enthalpy of a reaction or phase change.

In thermochemistry, we often need to calculate how many moles of a substance we have to determine the heat change per mole. For instance, to calculate the enthalpy of vaporization, you must know the number of moles, which can be found by dividing the mass of the substance by its molar mass:\[ n = \frac{m}{M} \], where \( n \) is the number of moles, \( m \) is the mass in grams, and \( M \) is the molar mass in grams per mole.