Question

How many kilojoules are given off when \(17.8 \mathrm{~mol}\) of \(\mathrm{CH}_{4}(\mathrm{~g})\) react? \(\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \Delta H=-890.1 \mathrm{~kJ}\)

Short answer

15843.78 kJ is given off.

Step-by-step solution

Understanding the Reaction

The given reaction is the combustion of methane (\(\mathrm{CH}_{4}\)). It reacts with oxygen (\(\mathrm{O}_{2}\)) to form carbon dioxide (\(\mathrm{CO}_{2}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)). The enthalpy change (\(\Delta H\)) of this reaction is \(-890.1 \mathrm{~kJ}\) per mole of \(\mathrm{CH}_{4}\) combusted.

Determining the Total Enthalpy Change

Given that \(17.8\) moles of \(\mathrm{CH}_{4}\) react, we need to calculate the total energy released. Multiply the number of moles by the enthalpy change per mole: \[\text{Total energy} = 17.8 \text{ moles} \times (-890.1 \mathrm{~kJ/mol})\] This gives \[= -15843.78 \mathrm{~kJ}\].

Final Calculation and Interpretation

The negative sign indicates that the energy is released, not absorbed. Therefore, the amount of energy given off when \(17.8\) moles of \(\mathrm{CH}_{4}\) react is \(15843.78 \mathrm{~kJ}\).

Key concepts

Understanding Combustion Reactions

A combustion reaction is a type of chemical reaction where a substance reacts with oxygen, releasing energy in the form of heat and light. In these reactions, a fuel (usually a hydrocarbon) combines with oxygen to produce carbon dioxide and water. Such reactions are exothermic, meaning they release energy. This released energy can be significant, making combustion crucial for applications like heating and powering engines.

• Combustion reacts fuel with oxygen (O₂)
• Generates products like CO₂ and H₂O
• Releases heat, making it an exothermic process

Therefore, in any combustion reaction, observing energy output is key, as it defines the reaction's exothermic nature and practical application.

Exploring Methane Combustion

Methane (\( \mathrm{CH}_4 \)) is a simple alkane and the primary component of natural gas. Its combustion is a well-known reaction used to furnish energy for various applications, from home heating to electricity generation. The balanced chemical reaction for methane combustion is shown as:\[\mathrm{CH}_4(g) + 2 \mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) + 2 \mathrm{H}_2\mathrm{O}(\ell)\]Key points of methane combustion include:

• Combines one methane molecule with two oxygen molecules
• Generates one carbon dioxide and two water molecules
• Releases substantial amounts of energy (\(\Delta H = -890.1 \mathrm{~kJ/mol}\)) per mole of methane .

The efficiency of this reaction is why methane is heavily utilized as a fuel source.

Calculating Energy in Combustion Reactions

Energy calculation in combustion reactions involves determining the total energy change that occurs when a specific quantity of fuel combusts. For methane combustion, the enthalpy change (\(\Delta H\)) indicates the amount of energy released per mole. To find the total energy released when combusting multiple moles of fuel, multiply the moles by \(\Delta H\):

• Identify the number of moles reacting
• Multiply by the given \(\Delta H\) value:
  \[\text{Total Energy} = \text{moles} \times \Delta H\]
• Interpret the result; a negative value indicates heat release

For example, with \(17.8\) moles of methane combusting, the calculation is \(-15843.78 \mathrm{~kJ}\), representing energy released during the reaction. This calculations simplicity showcases how predictable combustion processes can be useful for everyday energy needs.