Problem 118 - Chemistry: An Atoms-Focused Approach

Question

Balance the following chemical equation, name the reactants and products, and calculate the enthalpy change under standard conditions. $$\mathrm{FeO}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H_{\mathrm{rxn}}^{\circ}= ?$$

Step-by-Step Solution

Answer

Answer: The balanced chemical equation for the reaction between iron (II) oxide (FeO) and oxygen gas (O2) forming iron (III) oxide (Fe2O3) is: $$2\mathrm{FeO}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2}\mathrm{O}_{3}(s)$$ The enthalpy change of the reaction under standard conditions is -280 kJ/mol.

Step 1: 1. Balance the chemical equation

To balance the chemical equation, we need to make sure that there are equal numbers of each element on both sides of the equation. In the given equation, $$\mathrm{FeO}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2}\mathrm{O}_{3}(s)$$ There are two Fe atoms in the product while there's just one in the reactants. So, we should put a 2 in front of FeO: $$2\mathrm{FeO}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2}\mathrm{O}_{3}(s)$$ Now, we have 4 oxygen atoms on both sides, so the balanced chemical equation is: $$2\mathrm{FeO}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2}\mathrm{O}_{3}(s)$$

Step 2: 2. Name the reactants and products

The reactants in the balanced chemical equation are: - Iron (II) oxide (FeO) - Oxygen gas (O2) The product of the reaction is: - Iron (III) oxide (Fe2O3)

Step 3: 3. Calculate the enthalpy change under standard conditions

To calculate the enthalpy change ΔH under standard conditions, we will use the following formula: $$\Delta H_{rxn}^\circ = \sum (\Delta H_f(\mathrm{products}) \times \text{moles}) - \sum (\Delta H_f(\mathrm{reactants}) \times \text{moles})$$ Using the standard enthalpies of formation ΔHf values from a reference, we have: $$\Delta H_f^{\circ}(\mathrm{FeO}) = -272\ \mathrm{kJ/mol}$$ $$\Delta H_f^{\circ}(\mathrm{O}_2) = 0\ \mathrm{kJ/mol}$$ $$\Delta H_f^{\circ}(\mathrm{Fe}_2\mathrm{O}_3) = -824\ \mathrm{kJ/mol}$$ Now, plugging these values into the formula, we get: $$\Delta H_{rxn}^\circ = [(-824 \times 1)] - [(-272\times 2) + (0\times1)]$$ $$\Delta H_{rxn}^\circ = -824 - (-544)$$ $$\Delta H_{rxn}^\circ = -280\ \mathrm{kJ/mol}$$ Hence, the enthalpy change of the reaction under standard conditions is -280 kJ/mol.

Key Concepts

Enthalpy Change

Understanding enthalpy change is crucial in chemistry. It represents the heat absorbed or released during a chemical reaction under constant pressure. Enthalpy change (\(\Delta H\)) tells us if a reaction is exothermic or endothermic. An exothermic reaction has a negative \(\Delta H\), indicating that heat is released to the surroundings. An endothermic reaction has a positive \(\Delta H\), meaning it absorbs heat.

If you need to calculate the enthalpy change, use the following formula:

• \(\Delta H_{\text{rxn}}^{\circ} = \sum (\Delta H_f(\text{products}) \times \text{moles}) - \sum (\Delta H_f(\text{reactants}) \times \text{moles})\)

This formula accounts for the standard enthalpy of formation (\(\Delta H_f^{\circ}\)) of each substance in the reaction. By knowing these values, we can determine how much energy is exchanged during the reaction process.

Reactants and Products

In chemical reactions, reactants are substances that undergo change, while products are the new substances formed. Identifying them in a balanced chemical equation is essential for understanding the reaction.

For the equation \(2\mathrm{FeO}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2}\mathrm{O}_{3}(s)\):

• Reactants: These are the starting materials. In our case, Iron (II) oxide (FeO) and Oxygen gas (\(\mathrm{O}_2\)).
• Products: These are formed from the reactants. Here, Iron (III) oxide (\(\mathrm{Fe}_2\mathrm{O}_3\)) is produced.

By balancing the equation, we ensure that the number of atoms for each element is the same on both sides of the equation. This represents the law of conservation of mass, stating that matter cannot be created or destroyed in a chemical reaction.

Standard Enthalpy of Formation

The standard enthalpy of formation (\(\Delta H_f^{\circ}\)) is a measure used in thermodynamics to appreciate the energy involved in forming a compound from its elemental states. It is measured under standard conditions, which are 298 K temperature and 1 atm pressure.

For example, the \(\Delta H_f^{\circ}\) for \(\mathrm{FeO}\) is -272 kJ/mol, while for iron (III) oxide (\(\mathrm{Fe}_2\mathrm{O}_3\)), it is -824 kJ/mol. Standard enthalpies of formation help us understand the energy changes when compounds form from their elemental origins.

These values are useful for calculating the overall enthalpy change in reactions. Plenty of them can be found in standard thermodynamic tables, making it easier for us to perform these calculations. Remember, elements in their natural state, like \(\mathrm{O}_2\), have an enthalpy of formation of 0, serving as a reference point for these calculations.