Problem 57 - General Chemistry

Question

Colorless nitric oxide, NO, combines with oxygen to form nitrogen dioxide, \(\mathrm{NO}_{2}\), a brown gas. $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) ; \Delta H=-114 \mathrm{~kJ} $$ What is the enthalpy change per gram of nitric oxide?

Step-by-Step Solution

Answer

The enthalpy change per gram of NO is approximately -1.90 kJ/g.

Step 1: Molar Mass of Nitric Oxide

Calculate the molar mass of nitric oxide (NO) using the atomic masses: Nitrogen (N) has an atomic mass of 14.01 g/mol, and Oxygen (O) is 16.00 g/mol. Add them: \[ \text{Molar mass of NO} = 14.01 \, \text{g/mol} + 16.00 \, \text{g/mol} = 30.01 \, \text{g/mol} \]

Step 2: Enthalpy Change per Mole

According to the reaction equation, 2 moles of NO combine with 1 mole of O2 to form 2 moles of NO2, releasing -114 kJ of energy.The enthalpy change per mole of NO is: \[ \frac{-114 \, \text{kJ}}{2 \, \text{mol NO}} = -57 \, \text{kJ/mol} \]

Step 3: Enthalpy Change per Gram

Convert the enthalpy change from per mole to per gram. Use the molar mass calculated in Step 1:\[ \text{Enthalpy change per gram of NO} = \frac{-57 \, \text{kJ/mol}}{30.01 \, \text{g/mol}} \approx -1.90 \, \text{kJ/g} \]

Key Concepts

Molar Mass Calculation

To solve problems involving chemical reactions, it's crucial to first understand molar mass. Molar mass is the mass of one mole of a given substance. It allows us to relate the mass of a substance to the amount in moles, which is necessary for quantifying how much of each substance is involved in a chemical reaction.

For nitric oxide (NO), calculating the molar mass involves adding the atomic masses of nitrogen and oxygen. Nitrogen has an atomic mass of 14.01 g/mol and oxygen is 16.00 g/mol. Therefore, the molar mass of NO is calculated as follows: \[ \text{Molar mass of NO} = 14.01 \, \text{g/mol} + 16.00 \, \text{g/mol} = 30.01 \, \text{g/mol} \]

This value is important because it allows us to convert between the mass of nitric oxide and moles, which is essential for understanding energy changes in a reaction.

Nitric Oxide

Nitric oxide (NO) is a simple molecule composed of one nitrogen atom and one oxygen atom. It is a colorless gas under typical conditions and plays various roles in environmental and biological processes.

In the context of chemical reactions, nitric oxide can act as a reactant that forms nitrogen dioxide (NO₂) when combined with oxygen. This reaction not only changes the chemical composition of the substances involved but also releases energy, as indicated by the enthalpy change. Understanding nitric oxide's properties and how it interacts with other elements is essential for atmospheric chemistry and pollution studies.

When NO reacts, it's important to consider factors like its reactivity and the conditions under which it forms different compounds, which are key to comprehending its behavior in reactions.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, and these processes can either absorb or release energy. The chemical equation \[ 2 \text{NO}(g) + \text{O}_2(g) \longrightarrow 2 \text{NO}_2(g) \] demonstrates the reaction where nitric oxide reacts with oxygen to produce nitrogen dioxide.

Key aspects of chemical reactions include balanced equations, which ensure the same number of each type of atom is present on both sides of the equation. This balance is essential for respecting the law of conservation of mass, which states that mass cannot be created or destroyed in a chemical reaction.

In our example, 2 moles of NO react with 1 mole of O₂, illustrating a stoichiometric ratio that can be used to calculate the amount of products produced and reactants consumed.

Thermochemistry

Thermochemistry is the study of the energy changes that occur during chemical reactions. It focuses on concepts such as enthalpy, which is a measure of heat content in a system. In the given reaction, the enthalpy change, denoted by \( \Delta H \), is -114 kJ. This negative sign indicates that the reaction is exothermic, meaning it releases energy into the surroundings.

The enthalpy change is often given per mole of reactant or product involved. For the provided reaction, the enthalpy change per mole of NO is \[ \frac{-114 \, \text{kJ}}{2 \, \text{mol NO}} = -57 \, \text{kJ/mol} \] representing the energy released when one mole of NO reacts with oxygen.

Understanding these energy changes is crucial in chemistry for predicting reaction behavior, calculating energy requirements or emissions, and designing industrial processes.