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 quantity of heat released for each mole of water formed is \( -445.5\ \mathrm{kJ/mol} \). b. The quantity of heat released for each mole of oxygen reacted is \( -445.5\ \mathrm{kJ/mol} \).

Step-by-step solution

Analyze the balanced reaction

The balanced chemical equation for the given reaction is: \( CH_4(g) + 2 O_2(g) \longrightarrow CO_2(g) + 2 H_2O(l) \) The stoichiometry of the reaction indicates that for every mole of methane (CH4) reacted, two moles of water (H2O) are formed, and two moles of oxygen (O2) are consumed. Therefore, we can use the given enthalpy change to determine the heat released per mole of water and per mole of oxygen.

Calculate the heat released per mole of water formed

We know the enthalpy change of the reaction is -891 kJ. This is the energy change when one mole of methane reacts with two moles of oxygen to produce one mole of carbon dioxide and two moles of water. We can now calculate the amount of heat released for each mole of water formed. Given that for 2 moles of H2O the heat released is -891 kJ, we can calculate the heat for 1 mole of H2O in the following way: Heat released per mole of H2O = \( \frac{-891\ \mathrm{kJ}}{2\ \mathrm{moles\ of\ H_2O}} \)

Calculate the heat released per mole of oxygen reacted

We know the enthalpy change of the reaction is -891 kJ. This is the energy change when one mole of methane reacts with two moles of oxygen to produce one mole of carbon dioxide and two moles of water. We can now calculate the amount of heat released for each mole of oxygen reacted. Given that for 2 moles of O2 the heat released is -891 kJ, we can calculate the heat for 1 mole of O2 in the following way: Heat released per mole of O2 = \( \frac{-891\ \mathrm{kJ}}{2\ \mathrm{moles\ of\ O_2}} \)

Calculate the values

Now, let's compute the values we've set up in steps 2 and 3. Heat released per mole of H2O: \( \frac{-891\ \mathrm{kJ}}{2\ \mathrm{moles\ of\ H_2O}} = -445.5\ \mathrm{kJ\ per\ mole\ of\ H_2O} \) Heat released per mole of O2: \( \frac{-891\ \mathrm{kJ}}{2\ \mathrm{moles\ of\ O_2}} = -445.5\ \mathrm{kJ\ per\ mole\ of\ O_2} \) In conclusion, a. The quantity of heat released for each mole of water formed is -445.5 kJ/mol. b. The quantity of heat released for each mole of oxygen reacted is -445.5 kJ/mol.

Key concepts

Thermochemistry

Thermochemistry is a branch of chemistry that deals with the heat involved in chemical reactions. It focuses on understanding energy changes, particularly heat energy, during chemical transformations. The energy change is quantified as enthalpy change (\( \Delta H \)), which expresses the heat absorbed or released in a reaction at constant pressure.
For example, in the reaction of methane with oxygen to produce carbon dioxide and water, an enthalpy change of \(-891\ \text{kJ}\) indicates that heat is released. This reaction is exothermic as the reactants lose heat, indicating energy conservation tells us the energy is transferred to the surroundings.
It's crucial to remember that an enthalpy change can provide insights into whether a reaction releases or absorbs heat, helping us understand energy flow in chemical processes.

Stoichiometry

In chemistry, stoichiometry is the calculation of reactants and products in chemical reactions. It utilizes balanced chemical equations to give precise relationships between different substances. By examining the coefficients of each component in a reaction, we can establish crucial quantitative relationships.
Taking the methane combustion reaction as an example:

• For every 1 mole of \( \text{CH}_4 \), 2 moles of \( \text{O}_2 \) are used, producing 1 mole of \( \text{CO}_2 \) and 2 moles of \( \text{H}_2 \text{O} \).

This stoichiometric relationship allows us to calculate the amount of heat released per mole of water or oxygen since each mole of methane reacting corresponds to a specific energy change. By dividing the total enthalpy change by these stoichiometric factors, we derive insights into the energetic consequences of the reaction at a finer scale.

Chemical Reactions

Chemical reactions involve the transformation of substances through the making and breaking of chemical bonds. Each reaction has a unique equation describing the reactants transforming into products, often involving a noticeable energy change. In the methane and oxygen example, methane (\( \text{CH}_4 \)) and oxygen (\( \text{O}_2 \)) react to form carbon dioxide (\( \text{CO}_2 \)) and water (\( \text{H}_2 \text{O} \)).

• Reactants like \( \text{CH}_4 \) and \( \text{O}_2 \) undergo rearrangement of electrons, leading to products \( \text{CO}_2 \) and \( \text{H}_2 \text{O} \).
• This rearrangement involves breaking the bonds in the reactants and forming new bonds in the products, accompanied by an energy change, captured as an enthalpy change.

Understanding chemical reactions enables predictions of both product amounts and energy changes, which hold great importance in applications such as energy production and material synthesis.

Heat Release

Heat release is a crucial aspect of exothermic reactions, where the system emits heat into its surroundings. This is characterized by a negative enthalpy change, signifying energy flow out of the reaction system.
In the example of methane combustion, the heat released is \(-891\ \text{kJ}\), indicating that the reaction not only transforms substances but also impacts the energy dynamics. By dividing this total heat energy by the number of moles of product formed or reactants consumed, we pinpoint the heat released per mole.
For instance:

• Heat released per mole of water (\( \text{H}_2 \text{O} \)) formed is calculated as \(-445.5\ \text{kJ/mol}\).
• Similarly, per mole of oxygen (\( \text{O}_2 \)) reacted, it's also \(-445.5\ \text{kJ/mol}\).

These calculations reveal the efficiency and capacity of the reaction in utilizing and transferring energy, key insights for fields like energy and environmental science.