Problem 41 - Chemistry The Central Science In Si Units

Question

The molar heat of combustion of gaseous cyclopropane is \(-2089 \mathrm{~kJ} / \mathrm{mol} ;\) that for gaseous cyclopentane is \(-3317 \mathrm{~kJ} / \mathrm{mol}\). Calculate the heat of combustion per \(\mathrm{CH}_{2}\) group in the two cases, and account for the difference.

Step-by-Step Solution

Answer

Cyclopropane: \(-696.33 \mathrm{\ kJ/mol}\); Cyclopentane: \(-663.40 \mathrm{\ kJ/mol}\). Cyclopropane has more ring strain, causing higher energy release per \(\mathrm{CH}_2\) group.

Step 1: Determine the number of CH2 groups in each compound

Cyclopropane is a three-membered carbon ring and can be represented as \(\mathrm{C}_3\mathrm{H}_6\). This means it has 3 \(\mathrm{CH}_2\) groups. Cyclopentane is a five-membered carbon ring and can be represented as \(\mathrm{C}_5\mathrm{H}_{10}\). This means it has 5 \(\mathrm{CH}_2\) groups.

Step 2: Calculate the heat of combustion per CH2 group for cyclopropane

The total heat of combustion for cyclopropane is \(\-2089 \mathrm{\ kJ/mol}\). We divide this by the number of \(\mathrm{CH}_2\) groups (3): \[\text{Heat of combustion per \(\mathrm{CH}_2\) group for cyclopropane} = \frac{-2089}{3} = -696.33 \mathrm{\ kJ/mol}\]

Step 3: Calculate the heat of combustion per CH2 group for cyclopentane

The total heat of combustion for cyclopentane is \(\-3317 \mathrm{\ kJ/mol}\). We divide this by the number of \(\mathrm{CH}_2\) groups (5): \[\text{Heat of combustion per \(\mathrm{CH}_2\) group for cyclopentane} = \frac{-3317}{5} = -663.40 \mathrm{\ kJ/mol}\]

Step 4: Compare and explain the difference

Cyclopropane has a higher heat of combustion per \(\mathrm{CH}_2\) group (\(-696.33 \mathrm{\ kJ/mol}\)) compared to cyclopentane (\(-663.40 \mathrm{\ kJ/mol}\)). This is due to the fact that cyclopropane has a highly strained three-membered ring, which stores more potential energy, leading to greater energy release upon combustion. The larger the ring, the less strain, and thus cyclopentane releases less energy per \(\mathrm{CH}_2\) group.

Key Concepts

Understanding Cyclopropane

Cyclopropane is a unique and interesting compound in the world of chemistry. It consists of a three-membered carbon ring, formally written as \( \mathrm{C}_3\mathrm{H}_6 \). The uniqueness of cyclopropane lies in its geometric structure. The ring is highly strained because the carbon atoms form angles significantly less than the ideal \( 109.5^{\circ} \) typically seen in tetrahedral carbon bonds. These strained angles lead to a compound that stores a substantial amount of potential energy.
This energy is released when cyclopropane undergoes combustion, making it release more energy per \( \mathrm{CH}_2 \) group compared to less strained rings like cyclopentane.

• Highly strained carbon ring.
• Contains 3 \( \mathrm{CH}_2 \) groups.
• Has around \(-696.33 \ \mathrm{kJ/mol} \) energy release per \( \mathrm{CH}_2 \) group during combustion.

Exploring Cyclopentane

Cyclopentane represents another cyclic compound with a five-membered carbon ring, represented as \( \mathrm{C}_5\mathrm{H}_{10} \). Comparing cyclopentane to cyclopropane, you notice its ring is less strained since it more closely approaches the ideal bonding angles found in tetrahedral geometry. Consequently, cyclopentane has a lower internal energy stored.
When it combusts, the energy released is less per \( \mathrm{CH}_2 \) group because the bonds are not as high in energy. While the total energy released will still be significant, it doesn't compare with the intense energy released by breaking the highly strained bonds in smaller rings like cyclopropane.

• Less strained 5-member carbon ring.
• Contains 5 \( \mathrm{CH}_2 \) groups.
• Releases approximately \(-663.40 \ \mathrm{kJ/mol} \) per \( \mathrm{CH}_2 \) group during combustion.

The Science of Energy Release in Combustion Reactions

Combustion reactions involve the rapid oxidation of a substance, releasing energy in the form of heat and often light. When combusting hydrocarbons like cyclopropane and cyclopentane, this reaction releases energy because the products formed (mainly carbon dioxide and water) have lower energy than the reactants.
A significant factor influencing the energy release during combustion is the strain in the bonds before the reaction starts. Cyclopropane's highly strained three-membered ring stores considerable potential energy, making it more reactive. As its strained bonds break, the potential energy is converted into thermal energy, resulting in greater energy release.

• Combustion involves the breaking of high-energy bonds and forming low-energy bonds.
• Energy release is impacted by the bond strain and ring size.
• Highly strained bonds like those in cyclopropane convert to energy efficiently.