Problem 103 - Chemistry: An Atoms-Focused Approach

Question

Without doing any calculations, predict which compound in each pair releases more energy during combustion: a. 1 mole of \(\mathrm{CH}_{4}\) or 1 mole of \(\mathrm{H}_{2}\) b. \(1 \mathrm{g}\) of \(\mathrm{CH}_{4}\) or \(1 \mathrm{g}\) of \(\mathrm{H}_{2}\)

Step-by-Step Solution

Answer

And which compound releases more energy when 1 gram of each is combusted? Answer: 1 mole of CH₄ (methane) releases more energy during combustion compared to 1 mole of H₂ (hydrogen). However, when considering 1 gram of each compound, 1 gram of H₂ releases more energy than 1 gram of CH₄.

Step 1: Analyze the combustion reaction for both compounds

In a combustion reaction, a compound reacts with oxygen to produce carbon dioxide and water as products. The general equation for the combustion of a hydrocarbon can be written as: $$\text{Hydrocarbon} + \text{O}_{2} \rightarrow \text{CO}_{2} + \text{H}_{2}\text{O}$$ For CH₄, the balanced combustion reaction is: $$\text{CH}_{4} + 2\text{O}_{2} \rightarrow \text{CO}_{2} + 2\text{H}_{2}\text{O}$$ For H₂, the balanced combustion reaction is: $$2\text{H}_{2} + \text{O}_{2} \rightarrow 2\text{H}_{2}\text{O}$$ Notice that for 1 mole of CH₄ and 1 mole of H₂, both reactions create the same number of moles of water.

Step 2: Compare energy release for 1 mole of each compound

Since both reactions produce the same number of moles of water and the energy released is similar for each reaction, we can conclude that for 1 mole of each compound, CH₄ will release more energy during combustion because it also forms 1 mole of CO₂, which contributes to the total energy release. Hence, for part (a), 1 mole of CH₄ releases more energy during combustion than 1 mole of H₂.

Step 3: Compare energy release for 1 gram of each compound

When comparing the energy released per gram of compound, it is useful to consider the molar masses of the compounds. The molar mass of CH₄ is \(12.01 + 4(1.01) = 16.05 \, \text{g/mol}\), while the molar mass of H₂ is \(2(1.01) = 2.02 \, \text{g/mol}\). Therefore, 1 gram of methane (CH₄) is equal to approximately \(\frac{1}{16.05}\) mole, while 1 gram of hydrogen (H₂) is equal to approximately \(\frac{1}{2.02}\) mole. Since there are more moles of H₂ in 1 gram compared to CH₄, this means that during the combustion of 1 gram, more energy will be released from H₂ as there are more moles of H₂ involved in the reaction. Hence, for part (b), 1 gram of H₂ releases more energy during combustion than 1 gram of CH₄.

Key Concepts

Energy Release

In combustion reactions, the energy release is a critical factor to examine, as it determines how much heat and work can be generated from the reaction. A combustion reaction occurs when a fuel reacts with oxygen, producing carbon dioxide, water, and releasing energy in the form of heat. The amount of energy released during combustion is directly related to the complete breakdown of the molecular bonds present in the compound.

There are key points to consider in energy release during combustion:

• The type of fuel: Different fuels release different amounts of energy due to their chemical structure.
• The number of moles of product formed: More products usually indicate more bonds breaking, which can release more energy.
• The type of products: For hydrocarbons, forming carbon dioxide and water releases significant energy.

When comparing 1 mole of methane (CH₄) and 1 mole of hydrogen (H₂), methane releases more energy in its combustion reaction due to the formation of both water and carbon dioxide, whereas hydrogen forms only water. This additional carbon dioxide formation in methane contributes to the greater energy release.

Moles and Molar Mass

Understanding moles and molar mass is fundamental in comparing energy release among different substances. A mole is a unit used to express the amount of a substance, and molar mass is the weight of that substance expressed in grams per mole.

To calculate molar mass, sum up the atomic masses of all atoms in a molecule:

• For methane (CH₄), its molar mass is calculated as follows: \( 12.01 + 4 \times 1.01 = 16.05 \, \text{g/mol} \).
• For hydrogen (H₂), it is \( 2 \times 1.01 = 2.02 \, \text{g/mol} \).

In energy-related problems, the concept of moles is crucial because the number of moles directly affects how much energy can be released. When the same weight of different substances is used – like 1 gram of CH₄ versus 1 gram of H₂ – the substance with a lower molar mass has more moles and, therefore, can potentially release more energy during combustion. In this case, hydrogen has more moles in 1 gram compared to methane, leading to a greater energy release.

Hydrocarbons

Hydrocarbons are organic compounds composed solely of carbon and hydrogen atoms. They serve as a primary source of fuel due to their high energy release upon combustion.

Hydrocarbons are categorized based on their structural characteristics and include:

• Alkanes, which are saturated hydrocarbons, such as methane (CH₄).
• Alkenes and alkynes, which are unsaturated hydrocarbons with double or triple bonds.

In combustion, hydrocarbons react with oxygen to produce carbon dioxide and water, releasing a significant amount of energy. This reaction can be generally represented as:
\[ \text{Hydrocarbon} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \]
As seen in the comparison between CH₄ and H₂, methane serves as an excellent example of a hydrocarbon releasing more energy due to forming both water and carbon dioxide during its combustion. Hydrocarbons like methane are widely used for energy due to their efficiency and the substantial energy they release, making them valuable in various energy applications.