Question

Challenge Sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right)\) is formed when sulfur dioxide (SO_{2} ) reacts with oxygen and water. a. Write the balanced chemical equation for the reaction. b. How many moles of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is produced from 12.5 \(\mathrm{moles}\) of \(\mathrm{SO}_{2} ?\) c. How many moles of \(\mathrm{O}_{2}\) are needed?

Short answer

a. The balanced chemical equation is: \(SO_2 + \frac{1}{2}O_2 + H_2 O \rightarrow H_2 SO_4\) b. 12.5 moles of H2SO4 are produced from 12.5 moles of SO2. c. 6.25 moles of O2 are needed for the reaction.

Step-by-step solution

Write the chemical equation

We need to write the chemical equation for the reaction between sulfur dioxide (SO2), oxygen (O2), and water (H2O) to form sulfuric acid (H2SO4). The unbalanced equation is: \[SO_2 + O_2 + H_2 O \rightarrow H_2 SO_4\]

Balance the chemical equation

To balance the chemical equation, adjust the coefficients in front of each molecule, so that the number of atoms of each element is equal on both sides of the equation. The balanced chemical equation is: \[SO_2 + \frac{1}{2}O_2 + H_2 O \rightarrow H_2 SO_4\]

Calculate the moles of H2SO4 produced

According to the balanced equation, 1 mole of SO2 produces 1 mole of H2SO4. So, if we have 12.5 moles of SO2, we can directly determine the moles of H2SO4 produced: \[12.5 \, moles \, SO_2 \times \frac{1 \, mole \, H_2 SO_4}{1\, mole \, SO_2} = 12.5 \, moles \, H_2 SO_4\]

Calculate the moles of O2 needed

According to the balanced equation, 1 mole of SO2 requires 0.5 moles of O2 for the reaction. We can use the given moles of SO2 to determine the moles of O2 needed: \[12.5 \, moles \, SO_2 \times \frac{0.5 \, moles \, O_2}{1\, mole \, SO_2} = 6.25 \, moles \, O_2\] To summarize: a. The balanced chemical equation is: \(SO_2 + \frac{1}{2}O_2 + H_2 O \rightarrow H_2 SO_4\) b. 12.5 moles of H2SO4 are produced from 12.5 moles of SO2. c. 6.25 moles of O2 are needed for the reaction.

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that deals with determining the quantities of substances involved in chemical reactions. It's a bit like a recipe: if you know you need two eggs per cake, you can work out how many eggs you need for fifty cakes. In chemistry, we use the balanced chemical equation as the 'recipe' to work out how much of each reactant is needed to produce a certain amount of product.

For students tackling stoichiometry, the main goal is to understand how to use the coefficients in a balanced chemical equation to determine the proportions of reactants and products. These coefficients tell us the ratios of the molecules that participate in the reaction. For example, in the balanced equation for the synthesis of sulfuric acid, the coefficients indicate that one molecule of sulfur dioxide reacts with half a molecule of oxygen to produce one molecule of sulfuric acid. This proportional relationship is crucial when calculating the moles of reactants or products in a reaction.

Sulfuric Acid Synthesis

Sulfuric acid (H2SO4) is a highly important industrial chemical used in various applications such as fertilizer production, mineral processing, oil refining, and chemical synthesis. The synthesis of sulfuric acid can be achieved through the contact process, which involves the reaction of sulfur dioxide (SO2) with oxygen to form sulfur trioxide, which is then absorbed in water to produce sulfuric acid. However, in our textbook exercise, we are focusing on the direct reaction of sulfur dioxide with oxygen and water.

The balanced chemical equation provides all necessary details: 1 molecule of sulfur dioxide reacts with half a molecule of oxygen in the presence of water to form 1 molecule of sulfuric acid. This reaction is a simplification of the actual industrial process but provides a clear example for learning stoichiometry.

Mole Concept

The mole concept is a foundational pillar in chemistry that helps us count particles at the atomic and molecular level. One mole is defined as Avogadro's number (approximately 6.022 x 10^23) of particles, which can be atoms, molecules, or ions. It's akin to counting eggs by the dozen; only here, we're counting atoms and molecules by the mole.

In stoichiometry, the mole concept allows us to translate the balanced chemical equation into measurable quantities. When the equation indicates that 1 mole of SO2 produces 1 mole of H2SO4, it's saying that 6.022 x 10^23 molecules of SO2 will react to form 6.022 x 10^23 molecules of H2SO4. By understanding moles, students can solve problems involving the mass of reactants and products, volume of gases at standard temperature and pressure (STP), and the concentration of solutions. For instance, knowing that 12.5 moles of SO2 yields an equivalent number of moles of H2SO4 is straightforward with a firm grasp of the mole concept.