Problem 15 - Chemistry and Chemical Reactivity

Question

Nitrogen monoxide reacts with oxygen to give nitrogen dioxide. $$ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) $$ (a) You wish to react \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) in the correct stoichiometric ratio. The sample of NO has a volume of 150 mL. What volume of \(\mathrm{O}_{2}\) is required (at the same pressure and temperature)? (b) What volume of \(\mathrm{NO}_{2}\) (at the same pressure and temperature) is formed in this reaction?

Step-by-Step Solution

Answer

75 mL of \( \mathrm{O}_2 \) is required and 150 mL of \( \mathrm{NO}_2 \) is formed.

Step 1: Understanding the Reaction

The balanced chemical equation for the reaction is \( 2 \mathrm{NO} + \mathrm{O}_2 \rightarrow 2 \mathrm{NO}_2 \). This equation tells us that two volumes of \( \mathrm{NO} \) react with one volume of \( \mathrm{O}_2 \) to produce two volumes of \( \mathrm{NO}_2 \).

Step 2: Determine Volume of O2 Required

Given that 150 mL of \( \mathrm{NO} \) is used, the stoichiometric coefficient ratio \( 2:1 \) between \( \mathrm{NO} \) and \( \mathrm{O}_2 \) indicates that we need half the volume of \( \mathrm{O}_2 \) as compared to \( \mathrm{NO} \). Thus, the required volume of \( \mathrm{O}_2 \) is \( \frac{150}{2} = 75 \) mL.

Step 3: Calculate Volume of NO2 Produced

The equation shows that the volume of \( \mathrm{NO}_2 \) produced is equal to the volume of \( \mathrm{NO} \) reacted, as they have the same stoichiometric coefficient (2:2). Therefore, the volume of \( \mathrm{NO}_2 \) produced is 150 mL.

Key Concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into different substances, called products. In the exercise, nitrogen monoxide (\( \mathrm{NO} \)) and oxygen (\( \mathrm{O}_2 \)) are the reactants, and nitrogen dioxide (\( \mathrm{NO}_2 \)) is the product. These reactions occur because of the rearrangement of atoms, where bonds are broken and new bonds are formed to create new molecules.

A chemical reaction often involves a change in energy, which can manifest as the release or absorption of heat. Such reactions can be exothermic (releasing heat) or endothermic (absorbing heat).

• Exothermic reactions release energy and can result in higher temperatures.
• Endothermic reactions absorb energy, often resulting in a drop in temperature.

The reaction between \( \mathrm{NO} \) and \( \mathrm{O}_2 \) is a simple but important example of how chemical reactions can be represented and measured in terms of volume, especially for gases which can be easily measured in volume terms at constant pressure and temperature.

Gas Volumes

Gases, unlike solids and liquids, are highly compressible and expand to fill their containers. They are measured in terms of volume, which is why the problem involves volumes of gases reacting under constant temperature and pressure. In the context of the given exercise, the gas laws help us to understand the changes in gas volumes during the reaction.

• According to Avogadro's law, equal volumes of all gases at the same temperature and pressure have the same number of molecules.
• This law helps us to predict the volume changes based on the chemical equation given.

During the reaction, 150 mL of \( \mathrm{NO} \) reacts and thus by the stoichiometric ratio, we can calculate the volume of \( \mathrm{O}_2 \) required and the \( \mathrm{NO}_2 \) produced:

• 150 mL of \( \mathrm{NO} \) needs 75 mL of \( \mathrm{O}_2 \) because every 2 volumes of \( \mathrm{NO} \) reacts with 1 volume of \( \mathrm{O}_2 \).
• 150 mL of \( \mathrm{NO}_2 \) will be produced as it is directly proportional to the volume of \( \mathrm{NO} \) used (as \( 2:2 \) ratio).

Understanding gas volumes through this approach simplifies predictions about the behavior of gases during chemical reactions.

Balanced Chemical Equations

Balanced chemical equations are essential in stoichiometry as they help to ensure the conservation of mass in a reaction. This means the number of atoms of each element is the same on both sides of the equation. Balancing is necessary to correctly predict the amounts of reactants needed and products formed.

The reaction given in the exercise is already balanced: \[2 \mathrm{NO}(\mathrm{g}) + \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\]Each coefficient in the balanced equation represents a stoichiometric ratio or proportion in which the molecules react or are produced. Here:

• Two moles of nitrogen monoxide react with one mole of oxygen to yield two moles of nitrogen dioxide.
• This balanced equation shows that for every two nitrogen monoxide molecules, one oxygen molecule is consumed, resulting in two nitrogen dioxide molecules.

This understanding helps in calculating specific volumes or masses of reactants and products, aligning with core concepts of stoichiometry, which is a key aspect of chemistry. By ensuring the equation is balanced, it is possible to reliably calculate the reactant and product quantities, which is fundamental for experiments and industrial processes.