Problem 26 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

A flame calorimeter is used to measure enthalpy changes in gaseous reactions. In order to calibrate a particular flame calorimeter, a quantity of methane was burned in oxygen to release \(12.54 \mathrm{kJ}\) of energy which resulted in a temperature rise of \(1.000 \mathrm{K}\) Using the same flame calorimeter, the combustion of \(0.02 \mathrm{mol}\) of butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\), raised the temperature by \(5.017 \mathrm{K}\) while combustion of the same amount of methylpropane caused a temperature rise of \(4.575 \mathrm{K}\) Calculate the enthalpy change of isomerization for the two butane isomers. (Section 13.5 )

Step-by-Step Solution

Answer

The enthalpy change of isomerization is \(-277.5 \text{ kJ/mol}\).

Step 1: Understand the Problem

We need to find the enthalpy change of isomerization for two isomers: butane and methylpropane. The given data include the heat released by burning methane, the temperature changes due to butane and methylpropane combustion, and the molar amounts combusted.

Step 2: Determine the calorimeter constant

The calorimeter constant (C) is the ratio of the energy released by the combustion to the temperature change it causes. Using the combustion of methane: \[ C = \frac{Q}{\Delta T} = \frac{12.54 \text{ kJ}}{1.000 \text{ K}} = 12.54 \text{ kJ/K} \] where \( Q \) is heat energy and \( \Delta T \) is temperature change.

Step 3: Calculate the energy released by butane combustion

Using the previously calculated calorimeter constant: \[ Q_{\text{butane}} = C \times \Delta T_{\text{butane}} = 12.54 \text{ kJ/K} \times 5.017 \text{ K} = 62.90 \text{ kJ} \] for \(0.02 \text{ mol}\), so \(q_{\text{butane}} = \frac{62.90 \text{ kJ}}{0.02 \text{ mol}} = 3145 \text{ kJ/mol}\).

Step 4: Calculate the energy released by methylpropane combustion

Similarly, calculate the energy released by methylpropane: \[ Q_{\text{methylpropane}} = C \times \Delta T_{\text{methylpropane}} = 12.54 \text{ kJ/K} \times 4.575 \text{ K} = 57.35 \text{ kJ} \] for \(0.02 \text{ mol}\), so \(q_{\text{methylpropane}} = \frac{57.35 \text{ kJ}}{0.02 \text{ mol}} = 2867.5 \text{ kJ/mol}\).

Step 5: Calculate the enthalpy change of isomerization

The enthalpy change of isomerization of butane to methylpropane is the difference in combustion energies: \[ \Delta H_{\text{isomerization}} = q_{\text{methylpropane}} - q_{\text{butane}} = 2867.5 \text{ kJ/mol} - 3145 \text{ kJ/mol} = -277.5 \text{ kJ/mol} \].

Key Concepts

Enthalpy Changes

Enthalpy changes are a measure of the heat energy change in a reaction at constant pressure. When a chemical reaction occurs, bonds are broken and formed, affecting the energy levels of the reactants and products. This difference in energy is the enthalpy change and is often symbolized by \( \Delta H \).
Enthalpy changes can be exothermic (releasing energy to the surroundings) or endothermic (absorbing energy from the surroundings).

• Exothermic reactions, like combustion, release heat, resulting in a negative \( \Delta H \).
• Endothermic reactions absorb heat, leading to a positive \( \Delta H \).

In calorimetry, specifically when using a flame calorimeter, we measure the heat released in a controlled environment to calculate enthalpy changes accurately.
This involves determining the calorimeter constant and using it with the temperature changes to find precise values for \( \Delta H \). Practical understanding of enthalpy changes is crucial for fields like thermodynamics and physical chemistry.

Isomerization

Isomerization is a fascinating concept in chemistry where molecules transform into isomers - compounds with the same chemical formula but different structural arrangements. This change can have significant energy considerations, evident in their enthalpy differences.
For example, butane and methylpropane are isomers of \( C_4H_{10} \).

• The transformation from one isomer to another involves changes in molecular arrangement.
• Such changes, like with butane and methylpropane, can entail enthalpy changes because of differences in bond energy.

In the given problem, the enthalpy change of isomerization is calculated by finding the difference in the enthalpy changes of combustion for the two isomers.
Understanding isomerization helps in fields like organic chemistry and industry applications where different isomers can result in varied properties and uses.

Combustion Reactions

Combustion reactions are a type of exothermic reaction where a fuel reacts with an oxidizing agent, often oxygen, to release heat and form combustion products like carbon dioxide and water. They are a common way to study energy changes due to their straightforward nature and extensive practical applications, such as powering engines or heating.

• In combustion of hydrocarbons like methane or butane, carbon and hydrogen atoms react with oxygen to form \( CO_2 \) and \( H_2O \).
• The energy released is a result of the bond differences between reactants and products.

For calorimetry calculations, the amount of heat given off during combustion helps determine both the calorimeter constant and an accurate enthalpy change for these reactions.
Knowledge of combustion reactions is essential for students studying energy processes and is applicable in fields from energy production to environmental science.

Flame Calorimeter

A flame calorimeter is an instrument used to measure the heat of reaction for combustible gases, making it invaluable for studying enthalpy changes in gaseous reactions like combustion. This tool provides a controlled environment to precisely measure the energy changes.
Here’s how it generally works:

• A known amount of substance is burned, and the resultant heat changes the temperature of a surrounding water bath or calorimeter.
• The calorimeter constant is crucial as it relates the heat energy to the observed temperature change for the system.
• In our exercise, this was found using methane to calibrate the calorimeter, which then allowed us to measure other reactions accurately.

The rise in temperature for the combustion process is directly related to the energy released, enabling calculations like the enthalpy of isomerization.
Using a flame calorimeter helps students and professionals obtain precise data necessary for understanding energetic aspects of chemical reactions.