9.149 Consider the reaction: 4 CO1g2 2 NO21g2 4 CO21g2 N21g2. Using the following information, determine ΔH° for the reaction at 25 °C. NO1g2 ΔH°f = + 91.3 kJ>mol CO21g2 ΔH°f = - 393.5 kJ>mol 2 NO1g2 + O21g2 S 2 NO21g2 ΔH° = - 116.2 kJ 2 CO1g2 + O21g2 S 2 CO21g2 ΔH° = - 566.0 kJ

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Identify the target reaction: \(4 \text{CO}(g) + 2 \text{NO}_2(g) \rightarrow 4 \text{CO}_2(g) + \text{N}_2(g)\).

Use Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps that lead to the overall reaction.

Write the given reactions and their enthalpy changes: \(2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g)\), \(\Delta H^\circ = -116.2 \text{ kJ}\) and \(2 \text{CO}(g) + \text{O}_2(g) \rightarrow 2 \text{CO}_2(g)\), \(\Delta H^\circ = -566.0 \text{ kJ}\).

Calculate the enthalpy change for the formation of \(\text{NO}_2(g)\) using the given \(\Delta H^\circ_f\) values: \(\Delta H^\circ_f(\text{NO}_2) = \Delta H^\circ_f(\text{NO}) + \Delta H^\circ(\text{reaction})\).

Combine the enthalpy changes of the steps to find \(\Delta H^\circ\) for the target reaction using the stoichiometry of the target reaction and the given reactions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Enthalpy of Formation (ΔH°f)

The enthalpy of formation (ΔH°f) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is a crucial value in thermodynamics, as it allows for the calculation of the overall enthalpy change in a reaction by providing a reference point for the energy content of reactants and products.

Hess's Law

Hess's Law states that the total enthalpy change for a 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 of a reaction by using known enthalpy changes of related reactions, making it essential for determining ΔH° in complex reactions.

Standard Conditions

Standard conditions refer to a set of specific conditions (usually 1 atm pressure and 25 °C) under which thermodynamic measurements are made. These conditions provide a consistent basis for comparing thermodynamic data, such as enthalpy changes, and are critical for accurately calculating ΔH° for reactions, ensuring that the results are reliable and comparable.

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