Question

Determine \(\Delta n_{\text {gas }}\) for each of the following reactions: (a) \(2 \mathrm{KClO}_{3}(s) \rightleftharpoons 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)\) (b) \(2 \mathrm{PbO}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{PbO}_{2}(s)\) (c) \(\mathrm{I}_{2}(s)+3 \mathrm{XeF}_{2}(s) \Longrightarrow 2 \mathrm{IF}_{3}(s)+3 \mathrm{Xe}(g)\)

Short answer

For (a) \( \backslash \Delta n_{\text {gas}} = 3 \), (b) \( \backslash \Delta n_{\text {gas}} = -1 \), (c) \( \backslash \Delta n_{\text {gas}} = 3 \).

Step-by-step solution

Understanding \(\backslash \Delta n_{\text {gas}}\) Concept

\(\backslash \Delta n_{\text {gas}}\) represents the change in the number of moles of gas during a chemical reaction. It is calculated as the difference between the moles of gaseous products and moles of gaseous reactants.

Analyzing Reaction (a)

For the reaction \(2 \, \text{KClO}_{3} (s) \rightarrow 2 \, \text{KCl} (s) + 3 \, \text{O}_{2} (g)\), there are no gaseous reactants and 3 moles of \(\text{O}_{2}\) gas as the product. Therefore, \(\backslash \Delta n_{\text {gas}} = 3 - 0 = 3\).

Analyzing Reaction (b)

For the reaction \(2 \, \text{PbO} (s) + \text{O}_{2} (g) \rightarrow 2 \, \text{PbO}_{2} (s)\), there is 1 mole of \(\text{O}_{2}\) gas as the reactant and no gaseous products. Therefore, \(\backslash \Delta n_{\text {gas}} = 0 - 1 = -1\).

Analyzing Reaction (c)

For the reaction \( \text{I}_{2} (s) + 3 \, \text{XeF}_{2} (s) \rightarrow 2 \, \text{IF}_{3} (s) + 3 \, \text{Xe} (g)\), there are no gaseous reactants and 3 moles of \(\text{Xe}\) gas as the product. Therefore, \(\backslash \Delta n_{\text {gas}} = 3 - 0 = 3\).

Key concepts

Chemical Reactions

A chemical reaction involves the transformation of reactants into products. These transformations often involve changes in the state of matter, including solids, liquids, and gases. In the context of calculating \( \Delta n_{\text {gas}} \), understanding the state of each substance is crucial.

In the chemical equations given:

• Reactants are substances that start a reaction.
• Products are substances formed as a result of the reaction.
• The states of matter are denoted by (s) for solids, (l) for liquids, (g) for gases, and (aq) for aqueous solutions.

Consider the reaction: \(2 \text{KClO}_{3}(s) \rightarrow 2 \text{KCl}(s) + 3 \text{O}_{2}(g)\). Here, potassium chlorate (\(2 \text{KClO}_{3}\)) breaks down into potassium chloride (\(2 \text{KCl}\)) and oxygen gas (\(3 \text{O}_{2}\)). Understanding each component's state helps in calculating the change in gas moles.

Balancing chemical equations ensures that the same number of each type of atom appears on both sides of the equation, maintaining the law of conservation of mass.

Moles of Gas

Moles measure the amount of a substance. In chemical reactions, particularly those involving gases, counting the moles accurately determines the quantitative outcome of the reaction.

The concept of \( \Delta n_{\text {gas}} \) focuses on the change in the number of moles of gas during a chemical reaction. To calculate \( \Delta n_{\text {gas}} \):

• Determine the moles of gaseous products (products that are in gas form).
• Determine the moles of gaseous reactants (reactants that are in gas form).
• Subtract the moles of gaseous reactants from the moles of gaseous products.

For example, in the reaction \(2 \text{PbO}(s) + \text{O}_{2}(g) \rightarrow 2 \text{PbO}_{2}(s)\), there is 1 mole of \(\text{O}_{2}\) as reactant and no gaseous products. Therefore, \( \Delta n_{\text {gas}} = 0 - 1 = -1\). This indicates a decrease of one mole of gas in the reaction.

Gaseous Products and Reactants

Identifying gaseous products and reactants correctly is essential in calculating \( \Delta n_{\text {gas}} \). The state of reactants and products in a chemical reaction determines whether they are included in the \( \Delta n_{\text {gas}} \) calculation.

Let's examine the third reaction: \( \text{I}_{2}(s) + 3 \text{XeF}_{2}(s) \rightarrow 2 \text{IF}_{3}(s) + 3 \text{Xe}(g)\).

• Here, iodine (\(\text{I}_{2}\)) and xenon difluoride (\(3 \text{XeF}_{2}\)) are solid reactants.
• Iodine trifluoride (\(2 \text{IF}_{3}\)) is a solid product.
• Xenon (\(3 \text{Xe}\)) is a gaseous product.

By identifying which substances are gases, you can easily calculate \( \Delta n_{\text {gas}} = 3 - 0 = 3\). This increase in gaseous moles shows that more gas is produced than consumed. Keeping track of the states of all reactants and products simplifies these calculations.