Question

Nitrogen monoxide, a gas recently found to be involved in a wide range of biological processes, reacts with oxygen to give brown \(\mathrm{NO}_{2}\) gas. $$2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-114.1 \mathrm{kJ}$$ Is this reaction endothermic or exothermic? If \(1.25 \mathrm{g}\) of NO is converted completely to \(\mathrm{NO}_{2}\), what quantity of heat is absorbed or evolved?

Short answer

The reaction is exothermic. 2.38 kJ of heat is evolved.

Step-by-step solution

Determine reaction type (endothermic/exothermic)

The sign of \( \Delta H_{\text{rxn}}^{\circ} \) indicates whether the reaction is endothermic or exothermic. A negative \( \Delta H_{\text{rxn}}^{\circ} \) means the reaction is exothermic because it releases heat.

Calculate moles of NO

To calculate the moles of NO, use the molar mass of NO, which is approximately 30.01 g/mol. Use the formula: \( \text{moles of NO} = \frac{1.25\, \text{g}}{30.01\, \text{g/mol}} \approx 0.0417\, \text{mol} \).

Use reaction stoichiometry to find heat per mole

According to the balanced equation, 2 moles of NO releases \(-114.1\, \text{kJ}\). Therefore, 1 mole of NO releases \( \frac{-114.1\, \text{kJ}}{2} \approx -57.05\, \text{kJ/mol} \).

Calculate total heat evolved

Multiply the moles of NO by the heat released per mole: \( 0.0417\, \text{mol} \times (-57.05\, \text{kJ/mol}) \approx -2.38\, \text{kJ} \). This is the total heat evolved.

Key concepts

Thermodynamics

Thermodynamics is the study of energy transformations in physical and chemical processes. An important concept in thermodynamics is the enthalpy change, represented as \( \Delta H \), which tells us about the heat exchange during a reaction. If \( \Delta H \) is negative, it implies an exothermic reaction where energy is released to the surroundings, often in the form of heat. On the other hand, a positive \( \Delta H \) indicates an endothermic reaction where energy is absorbed from the surroundings.

In the context of the reaction between nitrogen monoxide (NO) and oxygen (\( O_2 \)) to form nitrogen dioxide (\( NO_2 \)), the given \( \Delta H_{\text{rxn}}^{\circ} = -114.1 \; \text{kJ} \) indicates that the reaction is exothermic. This means when NO gases react with oxygen, they release heat energy, which correlates with thermodynamics principles explaining energy release during chemical reactions.

Reaction Stoichiometry

Reaction stoichiometry involves using the balanced chemical equation to relate the quantities of reactants and products. It allows us to predict the amounts of substances consumed or produced in a reaction using mole ratios.

In the equation \( 2 \; \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \; \text{NO}_2(g) \), the coefficients tell us that two moles of NO react with one mole of \( O_2 \) to produce two moles of \( NO_2 \). This means the reactants and products are present in a 2:1:2 ratio.

When we convert 1.25 grams of NO to moles using its molar mass (30.01 g/mol), we calculate \( 0.0417 \; \text{mol} \). The stoichiometric ratio helps us further calculate the heat evolved per mole of NO, which is essential for determining the total heat involved in the reaction. Stoichiometry is a powerful tool in chemical calculations, enabling precise predictions based on chemical equations.

Heat Evolution

Heat evolution refers to the amount of heat released or absorbed during a chemical reaction. In exothermic reactions, such as the conversion of nitrogen monoxide to nitrogen dioxide, heat is given off, which can be quantified using the reaction's enthalpy change.

From the balanced reaction equation, we know that reacting two moles of NO with one mole of \( O_2 \) releases \(-114.1 \; \text{kJ} \). Therefore, the heat evolved per mole of NO can be calculated as \( \frac{-114.1 \; \text{kJ}}{2} \approx -57.05 \; \text{kJ/mol} \).

• For the given 0.0417 moles of NO, the total heat evolved is computed by multiplying the moles by the heat released per mole, resulting in approximately \(-2.38 \; \text{kJ}\).

This process confirms how heat values are determined and calculated based on specific quantities involved in chemical reactions, providing insights into energy changes accompanying these reactions.