Problem 30 - Chemistry and Chemical Reactivity

Question

Acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\), is made industrially by the reaction of methanol and carbon monoxide. $$\begin{aligned}\mathrm{CH}_{3} \mathrm{OH}(\ell)+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\ell) & \\\& \Delta H_{\mathrm{rxn}}^{\circ}=-355.9 \mathrm{kJ}\end{aligned}$$ If you produce \(1.00 \mathrm{L}\) of acetic acid (density \(=\) \(1.044 \mathrm{g} / \mathrm{mL})\) by this reaction, what quantity of heat is evolved?

Step-by-Step Solution

Answer

Approximately 6179 kJ of heat is evolved.

Step 1: Calculate the mass of produced acetic acid

First, we need to find the mass of 1.00 L of acetic acid. Since the density of acetic acid is given as 1.044 g/mL, we can calculate the mass using the formula: \( \text{mass} = \text{volume} \times \text{density} \). Convert 1.00 L to mL (1 L = 1000 mL):\[\text{mass} = 1000 \, \text{mL} \times 1.044 \, \text{g/mL} = 1044 \, \text{g}\]

Step 2: Calculate moles of acetic acid produced

Next, we need to find the moles of acetic acid. Use the molar mass of acetic acid (\(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\)), which is approximately 60.05 g/mol:\[\text{moles of acetic acid} = \frac{1044 \, \text{g}}{60.05 \, \text{g/mol}} \approx 17.38 \text{ mol}\]

Step 3: Calculate heat evolved in the reaction

The given reaction enthalpy \(\Delta H^{\circ}_{\text{rxn}} = -355.9 \, \text{kJ/mol}\) indicates the amount of heat evolved per mole of reaction. Since the reaction produces one mole of acetic acid per mole of reaction, the same amount of heat is evolved per mole of acetic acid. Calculate the total heat evolved:\[\text{Heat evolved} = 17.38 \, \text{mol} \times (-355.9 \, \text{kJ/mol}) = -6179.042 \, \text{kJ}\]

Step 4: Present the final answer and interpretation

The negative sign indicates that the heat is evolved (exothermic reaction). Therefore, producing 1.00 L of acetic acid evolves about 6179 kJ of heat.

Key Concepts

Stoichiometry

Stoichiometry is a method in chemistry used to calculate quantities in chemical reactions. It involves using relationships between reactants and products through a balanced chemical equation. For this reaction:

• Methanol (\( \text{CH}_3\text{OH} \)) reacts with carbon monoxide (\( \text{CO} \)) to produce acetic acid (\( \text{CH}_3\text{CO}_2\text{H} \)).
• The balanced equation reflects that each mole of methanol and carbon monoxide produces exactly one mole of acetic acid, showing a simple 1:1:1 relationship in stoichiometric coefficients.

Stoichiometry enables us to calculate the number of moles from a given mass using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).
This step is crucial in determining how much of a reactant or product is involved, as seen in this example where we calculated moles of acetic acid from a given mass using its molar mass.

Thermochemistry

Thermochemistry deals with the study of heat changes that occur during chemical reactions. Each reaction either absorbs or releases energy, quantified as enthalpy change (\( \Delta H \)).
In the given exercise, the enthalpy of reaction (\( \Delta H^{\circ}_{\text{rxn}} \)) is \( -355.9 \, \text{kJ/mol} \). This means that 355.9 kJ of heat is released for every mole of acetic acid produced.
Knowing the enthalpy helps in calculating the total heat exchange in the reaction, given the number of moles of reactants. Thermochemistry is essential to predict energy requirements and outcomes, important in industrial applications where energy efficiency is key.
Overall, thermochemistry provides insights into how energy interacts with matter during chemical processes.

Exothermic Reactions

Exothermic reactions are chemical reactions that release heat, resulting in a temperature increase in the surrounding environment.
In an exothermic reaction, the energy released from forming product bonds is greater than the energy required to break reactant bonds.
In the example problem:

• The reaction between methanol and carbon monoxide to form acetic acid is exothermic, as indicated by the negative sign of the enthalpy change (\( \Delta H^{\circ}_{\text{rxn}} = -355.9 \, \text{kJ/mol} \)).
• This signifies that 6179 kJ of energy is released when producing 1.00 L of acetic acid, providing thermal energy for other processes or to be dispersed in the environment.

Exothermic reactions are widely used in industry for energy generation and are critical in many chemical applications due to their ability to provide useful heat.