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 \(a s\) 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 per mole of water (\(\mathrm{H}_{2}\mathrm{O}\)) formed is \(445.5\, \text{kJ/mol}\). b. The heat released per mole of oxygen (\(\mathrm{O}_{2}\)) reacted is \(445.5\, \text{kJ/mol}\).

Step-by-step solution

Identify the Givens

In the given balanced reaction: \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g)\longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\), the enthalpy change is \(-891 \mathrm{kJ}\). We need to determine the heat released per mole: a. For water (\(\mathrm{H}_{2}\mathrm{O}\)) b. For oxygen (\(\mathrm{O}_{2}\))

Calculate Heat Released per Mole of Water

First, we'll find the heat released per mole of water. According to the balanced reaction, 1 mole of \(\mathrm{CH}_{4}\) reacts with 2 moles of \(\mathrm{O}_{2}\) to form 2 moles of \(\mathrm{H}_{2}\mathrm{O}\). So, the heat released by the formation of 1 mole of water can be found using the given enthalpy change. \[\text{Heat released per mole of water} = \frac{-891\, \text{kJ}}{2\,\text{moles of }\mathrm{H}_{2}\mathrm{O}}\]

Solve for Heat Released per Mole of Water

Solve the expression to find the heat released per mole of water: \[\frac{-891\, \text{kJ}}{2 \text{ moles}} = -445.5\, \text{kJ/mol}\] Thus, \(445.5\, \text{kJ}\) of heat is released for each mole of water formed.

Calculate Heat Released per Mole of Oxygen

Now, we'll find the heat released per mole of oxygen. According to the balanced reaction, 1 mole of \(\mathrm{CH}_{4}\) reacts with 2 moles of \(\mathrm{O}_{2}\) to release the given heat. So, the heat released by the reaction of 1 mole of oxygen can also be found using the given enthalpy change. \[\text{Heat released per mole of oxygen} = \frac{-891\, \text{kJ}}{2\,\text{moles of }\mathrm{O}_{2}}\]

Solve for Heat Released per Mole of Oxygen

Solve the expression to find the heat released per mole of oxygen: \[\frac{-891\, \text{kJ}}{2 \text{ moles}} = -445.5\, \text{kJ/mol}\] Thus, \(445.5\, \text{kJ}\) of heat is released for each mole of oxygen reacted.

Answers

a. The heat released per mole of water (\(\mathrm{H}_{2}\mathrm{O}\)) formed is \(445.5\, \text{kJ/mol}\). b. The heat released per mole of oxygen (\(\mathrm{O}_{2}\)) reacted is \(445.5\, \text{kJ/mol}\).

Key concepts

Understanding Thermochemistry

Thermochemistry is a fascinating branch of chemistry that studies the heat involved in chemical reactions. When substances interact, they either absorb or release energy, which is often in the form of heat. Knowing how heat energy changes during reactions helps us understand how much energy is needed or released and is crucial in many practical applications.

In chemical reactions, this energy change is termed the 'enthalpy change'. It can be either positive or negative, signifying endothermic (heat absorbed) or exothermic (heat released) reactions, respectively. In the given exercise, we observe an exothermic reaction, where methane ( ext{CH}_4) reacts with oxygen ( ext{O}_2) releasing a significant amount of heat, -891 ext{kJ}. Knowing the enthalpy change allows chemists to predict whether a reaction will require or release heat, helping in synthesizing desirable products more efficiently.

Exploring Reaction Enthalpy

Reaction enthalpy refers to the heat change associated with a chemical reaction. The value provided for the reaction in the exercise (-891 ext{kJ}) indicates the energy released when one mole of methane is burned completely as written in the equation. This helps determine the energy efficiency of fuel by measuring how much heat is produced.

For practical applications, it's essential to know how much heat is released or absorbed per mole of reactant or product. In our exercise, we are calculating how much energy is discharged for each mole of water and oxygen involved. This involves dividing the total enthalpy change by the stoichiometric coefficients of the substances in the balanced equation. Grasping these concepts is vital not only for academic purposes but also for industrial and environmental contexts, where energy management and conservation are critical.

The Role of Chemical Reactions in Enthalpy Change

Chemical reactions lie at the heart of enthalpy change discussions. Each reaction involves unique enthalpy characteristics based on the molecules involved and the bonds formed or broken. For the conversion given in the exercise, methane reacts with oxygen to yield carbon dioxide and water. In this process, the bonds in ext{CH}_4 and ext{O}_2 break, while new bonds form in ext{CO}_2 and ext{H}_2 ext{O}.

Understanding these reactions requires balancing energy input and output. Energy is added to break old bonds, while energy is released when new bonds are formed. This is what results in either a net release or absorption of energy as an enthalpy change. Learning how to quantify these reactions in terms of heat change is crucial for predicting the behavior of chemical processes, which impacts everything from energy production methods to ecological effects.