Problem 41 - General Chemistry

Question

Methane, \(\mathrm{CH}_{4}\), is a major component of marsh gas. When \(0.5000\) mol methane burns to produce carbon dioxide and liquid water, \(-445.1 \mathrm{~kJ}\) of heat is released. What is this heat in kilocalories?

Step-by-Step Solution

Answer

-445.1 kJ equals approximately -106.4 kcal.

Step 1: Understand the Conversion Factor

To convert energy from kilojoules to kilocalories, use the conversion factor: 1 kcal = 4.184 kJ.

Step 2: Set Up the Conversion Equation

Since we are given that the combustion of 0.5000 mol of methane releases -445.1 kJ, we can use the conversion factor to convert this energy to kilocalories. The equation will look like this: \[ \text{Energy in kcal} = \frac{\text{Energy in kJ}}{4.184} \]

Step 3: Perform the Calculation

Substitute the given value of -445.1 kJ into the conversion equation: \[ \text{Energy in kcal} = \frac{-445.1}{4.184} \approx -106.375 \text{ kcal} \]

Step 4: Interpret the Result

The negative sign indicates the heat released during the combustion process. Convert the numerical value into calories for a final description: The reaction releases approximately -106.4 kcal.

Key Concepts

Energy Conversion

Energy conversion is an essential aspect of science, especially in chemistry. It refers to changing energy from one form to another. In this context, we are transforming thermal energy during a combustion reaction.
This helps in understanding how much energy is exchanged in reactions, such as when a chemical burns. For different applications, energy is often expressed in various units. The two common units of energy are kilojoules (kJ) and kilocalories (kcal).
Knowing the conversion factor between these units is important for calculations:

• 1 kcal = 4.184 kJ
• This relationship allows us to convert energy values easily

By understanding energy conversion in this exercise, we make sense of the energy released when burning methane.

Enthalpy of Combustion

The enthalpy of combustion is a thermochemistry concept that refers to the heat change when a substance combusts in the presence of oxygen. It is typically expressed per mole of fuel.
When methane combusts, it combines with oxygen to produce carbon dioxide and water. This process releases heat – an exothermic reaction.
The enthalpy change (ΔH) is usually negative, meaning that heat is released. In this exercise, burning 0.5000 mol of methane releases

• -445.1 kJ of heat, meaning the reaction strongly supports burning reactions

Understanding this concept explains why methane is used as a fuel because its combustion releases significant energy.

Methane Combustion

Methane combustion is a chemical reaction where methane (\( \text{CH}_4\)) burns in oxygen to form carbon dioxide and water. This reaction is essential in many applications such as heating and power generation.
The reaction equation for methane combustion is:

• 
  \[\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}\]

This reaction is fundamental because:

• It demonstrates the conversion of chemical energy into thermal energy
• Shows that products are in more stable form than reactants

Understanding methane combustion is crucial for appreciating how carbon-based fuels can release substantial amounts of energy.

Heat Release

Heat release in chemical reactions is crucial to understand because it tells us how much energy is given off, often as thermal energy, making it an exothermic reaction.
During the combustion of methane, the release of energy reflects the difference in stored energy between reactants and products. This helps in energy management and efficiency calculations.
The negative sign in the heat release, like -106.4 kcal in our exercise, indicates heat is released rather than absorbed. Key points to remember:

• Exothermic reactions release heat, often making surroundings warmer
• Thermochemistry helps us understand energy exchange in natural and industrial processes

By grasping the concept of heat release, we gain deeper insight into energy dynamics in chemical reactions.