Given the data N₂(g) + O₂(g) → 2 NO(g) ΔH = +180.7 kJ 2 NO(g) + O₂(g) → 2 NO₂(g) ΔH = -113.1 kJ 2 N₂O(g) → 2 N₂(g) + O₂(g) ΔH = -163.2 kJ use Hess's law to calculate ΔH for the reaction N₂O(g) + NO₂(g) → 3 NO(g)

Verified step by step guidance

1. Identify the target reaction: \( \text{N}_2\text{O}(g) + \text{NO}_2(g) \rightarrow 3 \text{NO}(g) \).
2. Write down the given reactions and their enthalpy changes: \( \text{N}_2(g) + \text{O}_2(g) \rightarrow 2 \text{NO}(g) \), \( \Delta H = +180.7 \text{ kJ} \); \( 2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g) \), \( \Delta H = -113.1 \text{ kJ} \); \( 2 \text{N}_2\text{O}(g) \rightarrow 2 \text{N}_2(g) + \text{O}_2(g) \), \( \Delta H = -163.2 \text{ kJ} \).
3. Reverse the third reaction to match the target reaction's reactants: \( 2 \text{N}_2(g) + \text{O}_2(g) \rightarrow 2 \text{N}_2\text{O}(g) \), changing \( \Delta H \) to \(+163.2 \text{ kJ} \).
4. Adjust the stoichiometry of the reactions to match the target reaction: Divide the first reaction by 2 to get \( \text{N}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{NO}(g) \), and divide the second reaction by 2 to get \( \text{NO}(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{NO}_2(g) \).
5. Combine the adjusted reactions to form the target reaction, ensuring that the intermediates cancel out, and sum the enthalpy changes to find \( \Delta H \) for the target reaction.

Key Concepts

Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the sum of the enthalpy changes for the individual steps of the reaction, regardless of the pathway taken. This principle allows chemists to calculate the enthalpy change for a reaction that may be difficult to measure directly by using known enthalpy changes of related reactions.

Enthalpy Change (ΔH)

Enthalpy change (ΔH) is a measure of the heat content of a system at constant pressure. It indicates whether a reaction is exothermic (releases heat, ΔH < 0) or endothermic (absorbs heat, ΔH > 0). Understanding ΔH is crucial for predicting the energy changes associated with chemical reactions and for applying Hess's Law effectively.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It is essential for determining the proportions of substances involved in reactions, which is necessary when applying Hess's Law to combine multiple reactions and find the overall enthalpy change for a target reaction.