Problem 15 - Chemistry and Chemical Reactivity

Question

Nitrogen monoxide reacts with oxygen to give nitrogen dioxide. $$2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})$$ (a) If you mix \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) in the correct stoichiometric ratio, and NO has a volume of \(150 \mathrm{mL}\), what volume of O, is required (at the same pressure and temperature)? (b) After reaction is complete between 150 mL of \(\mathrm{NO}\) and the stoichiometric volume of \(\mathrm{O}_{2},\) what is the volume of \(\mathrm{NO}_{2}\) (at the same pressure and temperature)?

Step-by-Step Solution

Answer

75 mL of \( \text{O}_2 \) is required, and 150 mL of \( \text{NO}_2 \) is produced.

Step 1: Write the Balanced Equation

First, identify the balanced chemical equation for the reaction: \[ 2 \text{NO} + \text{O}_2 \rightarrow 2 \text{NO}_2 \].

Step 2: Understand Volume Ratios from Balanced Equation

From the balanced equation, we see that 2 volumes of \( \text{NO} \) react with 1 volume of \( \text{O}_2 \) to produce 2 volumes of \( \text{NO}_2 \).

Step 3: Calculate Volume of O2 Required

Given that the volume of \( \text{NO} \) is 150 mL, use the stoichiometric ratio to find the volume of \( \text{O}_2 \). According to the equation, 2 parts of \( \text{NO} \) react with 1 part of \( \text{O}_2 \). Thus, the volume of \( \text{O}_2 \) required is half of that of \( \text{NO} \): \( 150 \text{ mL} \times \frac{1}{2} = 75 \text{ mL} \).

Step 4: Calculate Volume of NO2 Produced

Since 2 volumes of \( \text{NO} \) are initially present, they will produce an equal volume of \( \text{NO}_2 \). Thus, the volume of \( \text{NO}_2 \) produced is the same as the volume of \( \text{NO} \) reacted, which is 150 mL.

Key Concepts

Chemical equations

Chemical equations are symbolic representations of chemical reactions. They show which chemicals are involved in a reaction and how they change to form new products. For example, the equation \(2 \text{NO} + \text{O}_2 \rightarrow 2 \text{NO}_2 \) represents the reaction between nitrogen monoxide and oxygen to produce nitrogen dioxide.

To correctly represent a reaction, chemical equations must be balanced. This means there are equal numbers of each type of atom on both sides of the equation. In our example, there are two nitrogen atoms and four oxygen atoms on each side, ensuring that mass is conserved.

Balancing equations often requires adjusting coefficients (the numbers in front of molecules or atoms) to achieve this equality. This is essential for calculations in stoichiometry, as it provides the reactant-to-product ratios necessary for determining quantities like reactant masses or product volumes.

Gas volumes

Gas volumes are crucial in chemical reactions involving gases, such as the one in our exercise, where both reactants and products are gases. According to Avogadro’s Law, under the same conditions of temperature and pressure, equal volumes of gases contain an equal number of molecules. This is why the balanced equation \(2 \text{NO} + \text{O}_2 \rightarrow 2 \text{NO}_2 \) can directly relate to volume ratios.

In this context, the equation indicates that 2 volumes of nitrogen monoxide (\(\text{NO}\)) react with 1 volume of oxygen (\(\text{O}_2\)) to produce 2 volumes of nitrogen dioxide (\(\text{NO}_2\)).

Thus, if you start with 150 mL of \(\text{NO}\), you'd require half the volume of \(\text{O}_2\), which is 75 mL, because the ratio between \(\text{NO}\) and \(\text{O}_2\) is 2:1.

Similarly, the volume of \(\text{NO}_2\) produced will match the initial volume of \(\text{NO}\), giving 150 mL of \(\text{NO}_2\). This illustrates the straightforward correlation between gas volumes and balanced equations when conditions are constant.

Reactant-product ratios

Reactant-product ratios are determined by the coefficients in a balanced chemical equation. These ratios are fundamental in stoichiometry, helping chemists calculate how much reactant is needed or how much product will form.

In the reaction \(2 \text{NO} + \text{O}_2 \rightarrow 2 \text{NO}_2\), the stoichiometric coefficients show a 2:1:2 ratio. This means:

• 2 volumes of \(\text{NO}\) require 1 volume of \(\text{O}_2\).
• The 2 volumes of \(\text{NO}\) will yield 2 volumes of \(\text{NO}_2\).

Understanding these ratios is crucial, as they allow us to determine the exact proportions of reactants and products without excessive calculation.

In the exercise example, the ratio dictated that 75 mL of \(\text{O}_2\) would react with 150 mL of \(\text{NO}\). After the reaction, 150 mL of \(\text{NO}_2\) is produced. These straightforward calculations highlight the utility of reactant-product ratios in predicting and understanding chemical reactions.