Problem 96 - General Chemistry

Question

Acetic acid, \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), is the sour constituent of vinegar (acetum is Latin for "vinegar"). In an experiment, \(3.58 \mathrm{~g}\) of acetic acid was burned. $$ \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l)+2 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ If \(52.0 \mathrm{~kJ}\) of heat evolved, what is \(\Delta H\) per mole of acetic acid?

Step-by-Step Solution

Answer

\(\Delta H \approx -872.14 \text{ kJ/mol}\)

Step 1: Convert Mass to Moles

First, determine the molar mass of acetic acid, HC extsubscript{2}H extsubscript{3}O extsubscript{2}. The molar mass is calculated as follows: C (2 atoms) is 2 × 12.01 g/mol, H (4 atoms) is 4 × 1.008 g/mol, and O (2 atoms) is 2 × 16.00 g/mol. Thus, the molar mass of acetic acid is 60.05 g/mol. Then convert the mass of acetic acid burned in the experiment to moles:\[ \text{Moles of } \text{HC}_2\text{H}_3\text{O}_2 = \frac{3.58 \text{ g}}{60.05 \text{ g/mol}} \approx 0.0596 \text{ mol} \]

Step 2: Calculate ΔH for the Reaction

The given heat evolved from burning 3.58 g of acetic acid is 52.0 kJ. Since the question asks for the enthalpy change per mole, we need to calculate the heat change for one mole of acetic acid. This is done by dividing the total heat evolved by the number of moles of acetic acid that were burned:\[ \Delta H = \frac{52.0 \text{ kJ}}{0.0596 \text{ mol}} \approx 872.14 \text{ kJ/mol} \]

Step 3: Interpret the Result

As the reaction releases heat, it is exothermic. Thus, the enthalpy change, \(\Delta H\), should be negative to indicate that it releases energy. Incorporate this sign:\[ \Delta H \approx -872.14 \text{ kJ/mol} \]

Key Concepts

Acetic Acid Combustion

Acetic acid combustion is a process where acetic acid reacts with oxygen to produce carbon dioxide and water. In the chemical equation given, acetic acid (\( \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l) \)) reacts with oxygen (\( \mathrm{O}_{2}(g) \)) to form carbon dioxide (\( \mathrm{CO}_{2}(g) \)) and water (\( \mathrm{H}_{2} \mathrm{O}(l) \)).When performing combustion:

• One molecule of acetic acid requires two molecules of oxygen to combust completely.
• The products of this reaction are always carbon dioxide and water.
• The reaction releases energy in the form of heat, which is measured as the heat evolved.

These properties make it a classic example of a combustion reaction. This specific reaction is important in studying enthalpy changes since it provides insights into the heat exchange during chemical transformations.

Molar Mass Calculation

To solve problems involving chemistry reactions, especially when dealing with enthalpy changes, it’s vital to calculate the molar mass correctly. Molar mass represents the mass of one mole of a substance, usually expressed in grams per mole (g/mol).Let's understand it with acetic acid:

• A molecule of acetic acid (\( \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \)) consists of:
  • 2 Carbon (C) atoms with a mass of 12.01 g/mol each, totaling 24.02 g/mol,
  • 4 Hydrogen (H) atoms at 1.008 g/mol each, totaling 4.032 g/mol,
  • 2 Oxygen (O) atoms with a mass of 16.00 g/mol each, totaling 32.00 g/mol.
• Adding these gives acetic acid a molar mass of 60.05 g/mol.

This calculation allows us to convert from grams to moles, a crucial step in determining the enthalpy change from the experimental data.

Exothermic Reactions

Exothermic reactions are types of chemical reactions that release energy, usually in the form of heat. In these reactions, the energy needed to break the bonds in the reactants is less than the energy released when new bonds form in the products.Important aspects:

• Heat is a byproduct, making the surroundings warmer.
• The enthalpy change (\( \Delta H \)) is negative, indicating that energy exits the system.
• Common examples include combustion reactions, like the acetic acid combustion.

In the exercise provided, the acetic acid combustion is clearly exothermic, as it involves the evolution of 52.0 kJ of heat. By calculating the enthalpy change per mole, we establish that the enthalpy change for the reaction is \( \Delta H \approx -872.14 \text{ kJ/mol} \), confirming the release of energy.