Problem 124 - General Chemistry

Question

Sulfur dioxide gas reacts with oxygen, \(\mathrm{O}_{2}(\mathrm{~g})\), to produce \(\mathrm{SO}_{3}(g)\). This reaction releases \(99.0 \mathrm{~kJ}\) of heat (at constant pressure) for each mole of sulfur dioxide that reacts. Write the thermochemical equation for the reaction of 2 mol of sulfur dioxide, and then also for the decomposition of \(3 \mathrm{~mol}\) of sulfur trioxide gas into oxygen gas and sulfur dioxide gas. Do you need any other information to answer either question?

Step-by-Step Solution

Answer

No additional information is needed. The equations are: \(2 \text{ SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{ SO}_{3}(g); \Delta H = -198.0 \text{ kJ}\) and \(3 \text{ SO}_{3}(g) \rightarrow 3 \text{ SO}_{2}(g) + \frac{3}{2} \text{O}_{2}(g); \Delta H = +297.0 \text{ kJ}\).

Step 1: Write the Thermochemical Equation for the Reaction of 2 mol SO2

Start with the standard form of the reaction: \(2 \text{ SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{ SO}_{3}(g)\). For each mole of \(\text{SO}_2\) reacting, \(99.0 \text{ kJ}\) of heat is released. Since 2 moles of \(\text{SO}_2\) are reacting, the total heat change is \(2 \times 99.0 = 198.0 \text{ kJ}\). Thus, the thermochemical equation is: \(2 \text{ SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{ SO}_{3}(g); \Delta H = -198.0 \text{ kJ}\).

Step 2: Write the Thermochemical Equation for Decomposition of 3 mol SO3

The decomposition reaction is the reverse of the synthesis reaction: \(2 \text{ SO}_{3}(g) \rightarrow 2 \text{ SO}_{2}(g) + \text{O}_{2}(g)\). For the decomposition, it requires \(198.0 \text{ kJ}\) to decompose 2 moles of \(\text{SO}_3\). Since the problem involves 3 moles of \(\text{SO}_3\), set up the proportion: \( \frac{198.0 \text{ kJ}}{2 \text{ mol}} \times 3 \text{ mol} = 297.0 \text{ kJ}\) absorbed. Thus, the thermochemical equation is: \(3 \text{ SO}_{3}(g) \rightarrow 3 \text{ SO}_{2}(g) + \frac{3}{2} \text{O}_{2}(g); \Delta H = +297.0 \text{ kJ}\).

Step 3: Determine If Additional Information Is Needed

The information given is sufficient to write the thermochemical equations since it specifies the heat change for the assumed reactions. No additional data is required beyond the given heat release per mole of \(\text{SO}_2\) reacting and the stoichiometry to modify the equations accordingly.

Key Concepts

Sulfur Dioxide Reaction

Sulfur dioxide (\(\text{SO}_2\)) is a reactive gas that can readily react with oxygen (\(\text{O}_2\)) to form sulfur trioxide (\(\text{SO}_3\)). This chemical reaction is an example of a synthesis process, where simpler molecules combine to form a more complex one.
In the reaction, each mole of sulfur dioxide is crucial as it combines in a specific ratio with oxygen to form sulfur trioxide.
Here is the balanced chemical equation for this reaction: \[2 \text{ SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{ SO}_{3}(g)\]

• 2 moles of \(\text{SO}_2\) react with 1 mole of \(\text{O}_2\).
• This leads to the production of 2 moles of \(\text{SO}_3\).

Understanding the fundamental structure of this reaction helps in determining its implications, such as energy change during the reaction.

Heat Change in Reactions

In chemical reactions, especially those involving gases like \(\text{SO}_2\), energy changes occur. This energy change can either be released as heat or absorbed from the surroundings.
For the reaction of sulfur dioxide with oxygen, heat is released, indicating an exothermic reaction.
This kind of reaction can be represented as: \(2 \text{ SO}_2(g) + \text{O}_2(g) \rightarrow 2 \text{ SO}_3(g); \Delta H = -198.0 \text{ kJ}\).

• The negative sign of \(\Delta H\) indicates heat release.
• The specific value tells us that 198.0 kJ of heat is released when 2 moles of \(\text{SO}_2\) react.

Understanding the energy aspect of a reaction is essential, as it influences reaction rates and conditions.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction.It is essentially a "recipe" for a chemical reaction, with reactants and products measured in moles.
In terms of our reaction: \[2 \text{ SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{ SO}_{3}(g)\]
We can infer the following stoichiometric relationships:

• 2 moles of \(\text{SO}_{2}\) react with 1 mole of \(\text{O}_2\).
• The product of this reaction is 2 moles of \(\text{SO}_3\).

By focusing on these relationships, stoichiometry allows chemists to predict the outcomes of reactions, measure reaction yields, and scale processes up or down effectively.

Chemical Decomposition

Chemical decomposition is the process by which a chemical compound breaks down into simpler compounds or elements.This is the opposite of a synthesis reaction.
For instance, when sulfur trioxide (\(\text{SO}_3\)) decomposes, it breaks back into sulfur dioxide (\(\text{SO}_2\)) and oxygen (\(\text{O}_2\)).
The balanced equation for the decomposition of 3 moles of \(\text{SO}_3\) is: \[3 \text{ SO}_{3}(g) \rightarrow 3 \text{ SO}_{2}(g) + \frac{3}{2} \text{O}_{2}(g); \Delta H = +297.0 \text{ kJ}\]

• This reaction absorbs heat, indicated by the positive \(\Delta H\).
• 297.0 kJ is absorbed for the decomposition of 3 moles of \(\text{SO}_3\).

Understanding decomposition reactions is vital as they are common in chemical processes such as degradation and recycling.

Enthalpy Change

Enthalpy change (\(\Delta H\)) is a measure of the total energy change during a chemical reaction.It includes internal energy and the work done by the system, often manifesting as heat.
In the sulfur dioxide reaction example, \(\Delta H\) signifies the exothermic nature of the reaction, releasing energy to the surroundings.
For decomposition, the \(\Delta H\) is positive, indicative of an endothermic process, where energy is absorbed:

• A negative \(\Delta H\) (e.g., -198.0 kJ) shows that heat is released.
• A positive \(\Delta H\) (e.g., +297.0 kJ) indicates that energy is absorbed.

Knowing the enthalpy change helps predict the energy requirements or releases, guiding energy management in chemical processes.