Question

Sulfur dioxide reacts with oxygen to form sulfur trioxide. (a) Write the balanced equation and use data from Appendix 2 to calculate \(\Delta H^{\circ}\) for this reaction. (b) At a given temperature and pressure, what volume of oxygen is required to react with \(1 \mathrm{~L}\) of sulfur dioxide? What volume of sulfur trioxide will be produced? (c) The diagram on the right represents the combination of equal volumes of the two reactants. Which of the following diagrams [(i)-(iv)] best represents the result?

Short answer

(a) \(\Delta H^{\circ} = -197.8\text{ kJ/mol}\). (b) 0.5 L of O₂ needed; 1 L SO₃ produced. (c) Diagram (iii) fits.

Step-by-step solution

Write the Balanced Chemical Equation

The reaction between sulfur dioxide (SO₃) and oxygen (O₂) to form sulfur trioxide (SO₃) is a standard chemical reaction. The balanced chemical equation is: \[ 2\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g) \] Each side of the equation has the same number of each type of atom, ensuring conservation of mass.

Calculate the Standard Enthalpy Change (\(\Delta H^{\circ}\))

To calculate \(\Delta H^{\circ}\) for the reaction, use the standard enthalpies of formation from Appendix 2: - \(\Delta H_f^{\circ}(\text{SO}_2(g)) = -296.8 \text{ kJ/mol} \)- \(\Delta H_f^{\circ}(\text{SO}_3(g)) = -395.7 \text{ kJ/mol} \)Apply the formula:\[ \Delta H^{\circ} = \sum(\Delta H_f^{\circ}\text{(products)}) - \sum(\Delta H_f^{\circ}\text{(reactants)}) \]\[ = [2(-395.7)] - [2(-296.8) + 0] \]\[ = [-791.4] - [-593.6] \]\[ = -197.8 \text{ kJ/mol} \] This means the reaction is exothermic.

Calculate Volumes for Part b

Assuming ideal gas behavior and that temperature and pressure are constant, use the stoichiometry of the balanced equation. - Since 2 volumes of SO₂ react with 1 volume of O₂, for 1 L of SO₂, \(\frac{1}{2}\) L of O₂ is required.- According to the balanced equation, 1 L of SO₂ produces 1 L of SO₃. Therefore, the reaction of 1 L SO₂ requires 0.5 L of O₂ and produces 1 L of SO₃.

Interpret the Diagram

Given that equal volumes of SO₂ and O₂ are combined, refer to the stoichiometry: - 2 volumes of SO₂ react with 1 volume of O₂. - With equal volumes of reactants, O₂ will be the limiting reactant. The reaction will consume all the O₂ and half of the SO₂, leaving excess SO₂. - Thus, half the volume of SO₂ remains unreacted and the diagram should show twice the initial amount of O₂ in SO₃. Diagram (iii) best represents this situation, with half the initial volume of SO₂ left unreacted.

Key concepts

Sulfur Dioxide

Sulfur dioxide, with the chemical formula \( ext{SO}_2\), is a gas that plays a critical role in numerous chemical processes. It arises primarily from the combustion of sulfur-containing compounds in fossil fuels and is considered a major air pollutant. In chemical reactions, \( ext{SO}_2\) acts as a precursor to sulfur trioxide \( ext{SO}_3\), which is a key component in the production of sulfuric acid.

• It is important to note that sulfur dioxide is a pungent gas, often used as a preservative in winemaking and in the production of some chemical compounds.
• The transformation of \( ext{SO}_2\) to \( ext{SO}_3\) is important industrially, especially in the creation of sulfuric acid which is utilized in fertilizers and detergents.

Understanding \( ext{SO}_2\) in these contexts aids in grasping its role in larger chemical equations and industrial applications.

Balanced Chemical Equation

In chemistry, a balanced chemical equation represents the principle of conservation of mass, where the number of atoms per element is equal on both sides of the reaction.
The balanced equation for the reaction between sulfur dioxide and oxygen is:\[2 ext{SO}_2(g) + ext{O}_2(g) \rightarrow 2 ext{SO}_3(g)\]When balancing, ensure that all chemical species have the same quantity of each element.

• In this reaction, every sulfur atom in the \( ext{SO}_2\) molecules finds a partner in the \( ext{SO}_3\) molecules on the product side.
• Oxygen in \( ext{O}_2\) is also balanced as it contributes to completing the \( ext{SO}_3\) molecules.
• Ultimately, the law of conservation ensures the masses are equal, maintaining the integrity of chemical reactions.

Mastering the art of balancing equations is crucial for solving stoichiometric problems that involve chemical reactions.

Enthalpy Change

Enthalpy change, denoted by \(\Delta H\), represents the heat change during a chemical reaction at constant pressure. For the sulfur dioxide reaction given, the standard enthalpy change \(\Delta H^{\circ}\) is calculated using enthalpies of formation.
Here’s the calculation formula:\[\Delta H^{\circ} = \sum(\Delta H_f^{\circ}\text{(products)}) - \sum(\Delta H_f^{\circ}\text{(reactants)})\]For our reaction:

• \(\Delta H_f^{\circ}(\text{SO}_2) = -296.8 \text{ kJ/mol} \)
• \(\Delta H_f^{\circ}(\text{SO}_3) = -395.7 \text{ kJ/mol} \)

Calculate as:\[[2(-395.7)] - [2(-296.8) + 0] = -197.8 \text{ kJ/mol}\]This negative value indicates an exothermic reaction, meaning it releases heat. Understanding enthalpy changes helps us predict energy flow in reactions.

Stoichiometry

Stoichiometry in chemistry refers to the calculation of reactants and products in chemical reactions. It involves using the coefficients in a balanced chemical equation to determine the relative amounts.
For the reaction \(2\text{SO}_2 + \text{O}_2 \rightarrow 2\text{SO}_3\):

• The stoichiometric ratios between the gases show that two molecules of \(\text{SO}_2\) react with one molecule of \(\text{O}_2\) to form two molecules of \(\text{SO}_3\).
• This implies that for every liter of \(\text{SO}_2\), half a liter (0.5 L) of \(\text{O}_2\) is needed and it results in one liter of \(\text{SO}_3\).
• This relationship allows us to predict the amounts of substances consumed and produced in the reaction under constant temperature and pressure.

By mastering stoichiometry, students can solve a broad array of problems, ensuring the practical application of chemistry concepts is precise and accurate.