Problem 86 - Chemistry The Science in Context

Question

Use the following standard heats of formation to calculate the molar enthalpy of vaporization of acetic acid: \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{CH}_{3} \mathrm{COOH}(\ell)\) is \(-484.5 \mathrm{~kJ} / \mathrm{mol}\) and \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{CH}_{3} \mathrm{COOH}(g)\) is \(-432.8 \mathrm{~kJ} / \mathrm{mol}\).

Step-by-Step Solution

Answer

Question: Calculate the molar enthalpy of vaporization for acetic acid, given the standard heats of formation for acetic acid in liquid and gaseous states: \(\Delta H_{\mathrm{f}}^\circ\) of \(\mathrm{CH}_{3} \mathrm{COOH}(\ell)\) is \(-484.5 \mathrm{~kJ} / \mathrm{mol}\) and \(\Delta H_{\mathrm{f}}^\circ\) of \(\mathrm{CH}_{3} \mathrm{COOH}(g)\) is \(-432.8 \mathrm{~kJ} / \mathrm{mol}\). Answer: The molar enthalpy of vaporization for acetic acid is \(51.7 \mathrm{~kJ} / \mathrm{mol}\).

Step 1: Recall the formula for enthalpy of vaporization

The formula we need to remember for the enthalpy of vaporization is: \(\Delta H_\text{vap} = \Delta H_\text{f}^\circ(\text{gaseous state}) - \Delta H_\text{f}^\circ(\text{liquid state})\)

Step 2: Identify the given values

We are given the standard heats of formation for both liquid and gaseous acetic acid: \(\Delta H_{\mathrm{f}}^\circ\) of \(\mathrm{CH}_{3} \mathrm{COOH}(\ell)\) is \(-484.5 \mathrm{~kJ} / \mathrm{mol}\) \(\Delta H_{\mathrm{f}}^\circ\) of \(\mathrm{CH}_{3} \mathrm{COOH}(g)\) is \(-432.8 \mathrm{~kJ} / \mathrm{mol}\)

Step 3: Use the formula to calculate the enthalpy of vaporization

Now, we will apply the formula to calculate the molar enthalpy of vaporization of acetic acid: \(\Delta H_\text{vap} = -432.8 \mathrm{~kJ} / \mathrm{mol} - (-484.5 \mathrm{~kJ} / \mathrm{mol})\)

Step 4: Calculate the final value

Simplify and solve the equation to get the enthalpy of vaporization: \(\Delta H_\text{vap} = -432.8 \mathrm{~kJ} / \mathrm{mol} + 484.5 \mathrm{~kJ} / \mathrm{mol} = 51.7 \mathrm{~kJ} / \mathrm{mol}\) The molar enthalpy of vaporization for acetic acid is \(51.7 \mathrm{~kJ} / \mathrm{mol}\).

Key Concepts

Acetic Acid

Acetic acid is a common chemical compound, known for its sour taste and pungent smell, familiar as the main component of vinegar. It's represented by the chemical formula \( \mathrm{CH}_3\mathrm{COOH} \). Understanding its properties is crucial for students dealing with chemistry problems, especially those related to phase changes like vaporization.

• Chemical Structure: Acetic acid consists of two carbon atoms, four hydrogen atoms, and two oxygen atoms, arranged such that it forms a carboxylic acid functional group.
• Physical Properties: At room temperature, acetic acid is a clear, colorless liquid. It freezes at 16.7°C and boils at 118°C.
• Uses: Acetic acid is widely used in food, pharmaceuticals, and as a chemical reagent in laboratories.

In the context of enthalpy of vaporization, understanding that acetic acid can exist in both liquid and gaseous states helps with calculating energy changes during phase transitions. The distinction between its physical states is key in thermodynamics. This involves measuring the heat required for transforming acetic acid from the liquid to the gas phase.

Standard Heat of Formation

The standard heat of formation is a fundamental concept in chemistry, crucial when calculating heats of reactions and phase changes. It's defined as the change in enthalpy when one mole of a substance is formed from its elements under standard conditions. This value is symbolized as \(\Delta H_{\mathrm{f}}^{\circ}\) .

• Significance: The standard heat of formation allows chemists to understand and predict the energy changes involved in chemical processes.
• Standard Conditions: It is measured under standard conditions of 1 atmosphere of pressure and a temperature of 25°C (298 K).
• Usage: These values are used extensively in calculations involving enthalpy changes, such as those in Hess's Law and Gibbs free energy considerations.

In this exercise, we are dealing with the standard heats of formation for both liquid and gaseous acetic acid. Knowing these values lets us calculate the enthalpy of vaporization, which is the difference between the gaseous and liquid phases under standard conditions. This provides insight into how much energy is required for the phase transition.

Enthalpy Calculation

Enthalpy calculations are a cornerstone of thermochemistry, assisting students in understanding energy changes in chemical reactions and phase transitions. To calculate the enthalpy of vaporization, one applies the formula: \(\Delta H_\text{vap} = \Delta H_{\mathrm{f}}^{\circ}(\text{gas}) - \Delta H_{\mathrm{f}}^{\circ}(\text{liquid}) \). This formula is derived from the idea that the vaporization process involves a transformation from liquid to gas.

• Understanding the Formula: The formula calculates the energy required to convert one mole of liquid into gas at constant temperature and pressure.
• Importance in Chemistry: Calculating enthalpy changes helps predict how substances interact and react under different conditions.
• Practical Application: These calculations are essential for industrial processes, where energy efficiency is crucial, and in designing new chemical reactions in research settings.

In the given problem, we take the standard heats of formation of acetic acid in its liquid and gaseous forms to find the energy needed for its vaporization. The process involves subtracting the \( \Delta H_{\mathrm{f}}^{\circ}\) of the liquid from that of the gas, leading to the calculated value of 51.7 kJ/mol. This reveals how much energy is involved in overcoming intermolecular forces during the phase change.