Question

The enthalpy change for the reaction $$ \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ is \(-891 \mathrm{~kJ}\) for the reaction as written. a. What quantity of heat is released for each mole of water formed? b. What quantity of heat is released for each mole of oxygen reacted?

Short answer

a. The heat released for each mole of water formed is -445.5 kJ/mol. b. The heat released for each mole of oxygen reacted is -445.5 kJ/mol.

Step-by-step solution

Analyze the given information

Given, the enthalpy change for the reaction: \[ \mathrm{CH}_{4}(g) + 2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + 2 \mathrm{H}_{2}\mathrm{O}(l) \] ΔH = -891 kJ

Determine heat released for each mole of water formed

Since two moles of water are formed in the reaction, we can calculate the heat released per mole of water. We'll divide the total heat released by the number of moles of water formed. Heat released per mole of water = \( \frac{\text{Total heat released}}{\text{Number of moles of water formed}} \) Heat released per mole of water = \( \frac{-891\,\text{kJ}}{2\,\text{moles}} \)

Calculate the heat released per mole of water formed

Heat released per mole of water = \( -\frac{891}{2} \,\text{kJ/mol} \) Heat released per mole of water = -445.5 kJ/mol So, for each mole of water formed, 445.5 kJ of heat is released (negative sign indicates that heat is released). Answer (a): -445.5 kJ/mol

Determine heat released for each mole of oxygen reacted

For every 2 moles of oxygen, the total heat released is -891 kJ. We can calculate the heat released per mole of oxygen by dividing the total heat released by the number of moles of oxygen reacted. Heat released per mole of oxygen = \( \frac{\text{Total heat released}}{\text{Number of moles of oxygen reacted}} \) Heat released per mole of oxygen = \( \frac{-891\,\text{kJ}}{2\,\text{moles}} \)

Calculate the heat released per mole of oxygen reacted

Heat released per mole of oxygen = \( -\frac{891}{2} \,\text{kJ/mol} \) Heat released per mole of oxygen = -445.5 kJ/mol So, for each mole of oxygen reacted, 445.5 kJ of heat is released (negative sign indicates that heat is released). Answer (b): -445.5 kJ/mol

Key concepts

Chemical Reaction Enthalpy

The term 'enthalpy change' in a chemical reaction refers to the amount of heat content that is either absorbed or released during the transformation of reactants into products. It is denoted by the symbol \( \Delta H \). If the process releases heat, such as in combustion reactions, it is exothermic and \( \Delta H \) is negative. Conversely, reactions that absorb heat from their surroundings are endothermic, and \( \Delta H \) is positive.

In our given exercise, the combustion of methane (\(\text{CH}_{4}(g)\)) with oxygen (\(\text{O}_{2}(g)\)) results in the production of carbon dioxide (\(\text{CO}_{2}(g)\)) and water (\(\text{H}_{2} \text{O}(l)\)), with an enthalpy change of \( -891 \text{ kJ} \). This negative \( \Delta H \) indicates that heat is released and the reaction is exothermic. Understanding how to calculate and interpret enthalpy changes allows students to predict the energy transfers within various chemical reactions.

Heat Released per Mole

The concept of 'heat released per mole' is crucial in thermochemistry, showing the amount of heat transfer associated with one mole of a reactant or product in a chemical reaction. It's a specific instance of the broader concept of molar enthalpy. The calculation typically involves dividing the total heat change by the number of moles of the specific substance being considered.

For example, the exercise demonstrates how to determine the heat released per mole of water (\(\text{H}_{2} \text{O}\)) and per mole of oxygen (\(\text{O}_{2}\)). The calculated values express the amount of energy, in kilojoules, that are released when one mole of water or oxygen takes part in the reaction. Reporting heat released per mole allows us to compare the energy profiles of different chemical substances on a per-mole basis, which is invaluable for scientists, especially when designing energy-efficient processes or understanding chemical energetics.

Thermochemistry

Thermochemistry is the branch of chemistry that studies the heat energy involved in chemical reactions and phase changes. The first law of thermodynamics, which states that energy cannot be created or destroyed, governs thermochemistry and ensures the conservation of energy within these processes.

As demonstrated in this exercise, thermochemistry involves determining the heat exchange between a system and its surroundings. In calculations, it's important to use consistent units and account for the stoichiometry of the reaction, as change in enthalpy is directly proportional to the quantity of reactants and products involved. The knowledge of thermochemistry is applied in various fields, such as predicting reaction spontaneity, engineering, and environmental studies, making it a foundational concept in both theoretical and applied chemistry.

Stoichiometry

Stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. It's grounded on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Hence, stoichiometry involves using the balanced chemical equation to determine the proportions of chemicals required or formed.

In the given exercise, stoichiometry helps to calculate the heat released per mole of products (e.g., water) or reactants (e.g., oxygen) based on the overall enthalpy change for the reaction. It provides a clear pathway to understand the conversion process of reactants to products and ensures that students grasp the concept of molar ratios and their practical utility in predicting the outcomes of chemical reactions, such as the exact amount of energy released per mole.