Question

One step in the commercial production of sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), involves the conversion of sulfur dioxide, \(\mathrm{SO}_{2},\) into sulfur trioxide, \(\mathrm{SO}_{3}\). $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g) $$ If \(150 \mathrm{~kg}\) of \(\mathrm{SO}_{2}\) reacts completely, what mass of \(\mathrm{SO}_{3}\) should result?

Short answer

When 150 kg of SO₂ reacts completely, 187.5 kg of SO₃ should be produced.

Step-by-step solution

Convert mass of SO₂ to moles

The molar mass of sulfur dioxide (SO₂) is 32.07 (S) + 2 × 16.00 (O) = 64.07 g/mol. We are given that 150 kg of SO₂ reacts completely. To convert this mass to moles, we can use the formula: moles = mass / molar mass So in this case, moles of SO₂ = \( \frac{150,000\,\text{g}}{64.07\,\text{g/mol}} \approx 2341.5\,\text{moles} \)

Use stoichiometry to find moles of SO₃

From the balanced chemical equation, we can see that 2 moles of SO₂ react with 1 mole of O₂ to produce 2 moles of SO₃. The stoichiometric ratio of SO₂ to SO₃ is 2:2, which simplifies to 1:1. Therefore, for each mole of SO₂ consumed, one mole of SO₃ is produced. So, the moles of SO₃ produced are equal to the moles of SO₂ consumed: moles of SO₃ = 2341.5 moles

Convert moles of SO₃ to mass

The molar mass of sulfur trioxide (SO₃) is 32.07 (S) + 3 × 16.00 (O) = 80.07 g/mol. Now we can convert the moles of SO₃ back to mass using the formula: mass = moles × molar mass mass of SO₃ = 2341.5 moles × 80.07 g/mol ≈ 187531.5 g = 187.5 kg (rounded to one decimal place) So, when 150 kg of SO₂ reacts completely, 187.5 kg of SO₃ should be produced.

Key concepts

Understanding Molar Mass

Molar mass is a central concept in stoichiometry, as it connects the mass of a substance to the amount in moles. It is defined as the mass of one mole of a given substance in grams. To find the molar mass, sum up the atomic masses of all atoms in a chemical formula.

For example, the molar mass of sulfur dioxide (\(\text{SO}_2\)) is calculated by adding:

• The atomic mass of one sulfur atom: 32.07 g/mol
• Twice the atomic mass of oxygen (since there are two oxygen atoms): 2 \(\times\) 16.00 g/mol

Thus, the molar mass of \(\text{SO}_2\) is 64.07 g/mol.

Similarly, for sulfur trioxide (\(\text{SO}_3\)), the molar mass would be 32.07 g/mol for sulfur plus three times 16.00 g/mol for the oxygen atoms, equalling 80.07 g/mol. Knowing these values allows us to convert between mass and moles, enabling us to predict the outcomes of chemical reactions.

Basics of Chemical Reactions

Chemical reactions involve the transformation of reactants into products. They are represented by balanced chemical equations that show the relationship between the molecules involved in the reaction. The balanced equation indicates the proportion or ratio in which substances react and form products.

In the equation \(2\, \text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\, \text{SO}_3(g)\), we see that sulfur dioxide reacts with oxygen to form sulfur trioxide. Here, the coefficients show that two moles of \(\text{SO}_2\) react with one mole of \(\text{O}_2\) to produce two moles of \(\text{SO}_3\).

This equation is balanced because the number of each type of atom is the same on both sides of the equation. Balanced equations allow chemists to calculate the necessary amounts of reactants and predict the amount of product formed.

The Process of Mole Conversion

Mole conversion is a technique used to transition between units of mass and moles. It is essential in stoichiometry because most chemical reactions are described in terms of moles.

When converting from mass to moles, use the formula:

• Moles = Mass / Molar Mass

For example, if you have 150 kg of \(\text{SO}_2\), convert it into grams (150,000 g) and then find the number of moles by dividing by its molar mass (64.07 g/mol), resulting in about 2341.5 moles of \(\text{SO}_2\).

Once in moles, stoichiometric ratios from a balanced equation allow conversion between substances. Since 1 mole of \(\text{SO}_2\) produces 1 mole of \(\text{SO}_3\), the moles of \(\text{SO}_3\) will also be 2341.5. To find the resulting mass of \(\text{SO}_3\), you multiply the moles by the molar mass of \(\text{SO}_3\) (80.07 g/mol), leading to a mass of 187.5 kg. This process helps accurately evaluate the quantities involved in chemical reactions.