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, approximately 187.47 kg of SO₃ should be produced.

Step-by-step solution

Calculate the molar mass of SO₂

To convert the mass of SO₂ into moles, we need to find the molar mass. For sulfur dioxide (SO₂), the molar mass is calculated as follows: - Sulfur: 32.07 g/mol - Oxygen: 2 × 16.00 g/mol (Since there are two oxygen atoms) So the molar mass of SO₂ is 32.07 + 2 * 16.00 = 64.07 g/mol.

Convert mass of SO₂ into moles

Now, we'll use the molar mass of SO₂ to convert the given mass of 150 kg into moles. First, we convert the mass from kg to g, remembering that 1 kg = 1000 g: 150 kg × 1000 g/kg = 150,000 g Now, we'll convert the mass into moles, using the molar mass of SO₂: \(moles\ of\ SO_{2} = \frac{mass\ of\ SO_{2}}{molar\ mass\ of\ SO_{2}}\) \(moles\ of\ SO_{2} = \frac{150,000\ g}{64.07\ g/mol} \approx 2341.75\ mol\)

Use stoichiometry to find moles of SO₃ produced

Using the stoichiometry of the balanced chemical equation, we can find the moles of SO₃ produced. The stoichiometry for SO₂:SO₃ in the chemical equation is 2:2, or 1:1, meaning 1 mole of SO₂ reacts to produce 1 mole of SO₃. So, the moles of SO₃ produced will be the same as the moles of SO₂ reacted, which is approximately 2341.75 mol.

Calculate the molar mass of SO₃

To convert moles of SO₃ into mass, we must calculate the molar mass of SO₃. For sulfur trioxide (SO₃), the molar mass is calculated as follows: - Sulfur: 32.07 g/mol - Oxygen: 3 × 16.00 g/mol (Since there are three oxygen atoms) So the molar mass of SO₃ is 32.07 + 3 * 16.00 = 80.07 g/mol.

Convert moles of SO₃ into mass

Finally, we'll use the molar mass of SO₃ to convert the moles of SO₃ produced into mass: \(mass\ of\ SO_{3} = moles\ of\ SO_{3} \times molar\ mass\ of\ SO_{3}\) \(mass\ of\ SO_{3} = 2341.75\ mol \times 80.07\ g/mol \approx 187,471.93\ g\) Since the mass is in grams, let's convert it to kilograms (remembering that 1 kg = 1000 g): \(mass\ of\ SO_{3} = \frac{187,471.93\ g}{1000\ g/kg} \approx 187.47\ kg\)

Final Answer

When 150 kg of SO₂ reacts completely, approximately 187.47 kg of SO₃ should be produced.

Key concepts

Molar Mass Calculation

Understanding the concept of molar mass is crucial for mastering stoichiometry, which is a key aspect of chemistry involving the calculation of reactants and products in chemical reactions. The molar mass is defined as the mass of one mole of a substance, and it is typically expressed in grams per mole (g/mol).

To calculate the molar mass of a compound, such as sulfur dioxide (SO₂), you would add up the atomic masses of all the atoms in the molecule. This is found using the periodic table: for SO₂, sulfur has an atomic mass of approximately 32.07 g/mol, while oxygen has an atomic mass of 16.00 g/mol. Since there are two oxygen atoms in sulfur dioxide, you would multiply the mass of oxygen by two and then add it to the mass of sulfur to find the molar mass of SO₂.

This process allows chemists to convert between mass and moles, a fundamental step in solving many chemistry problems.

Chemical Reaction Balancing

Balancing chemical equations is fundamental in stoichiometry as it ensures that the law of conservation of mass is obeyed; matter can neither be created nor destroyed. Every balanced equation provides a ratio of how much of one reactant is needed to react with another, or how much product is formed from the reactants.

Take the reaction of sulfur dioxide converting to sulfur trioxide as an example: the equation is balanced with a stoichiometric coefficient of 2 in front of both SO₂ and SO₃, indicating that 1 mole of SO₂ will produce 1 mole of SO₃. The oxygen molecule (O₂) also needs to be balanced, requiring a coefficient of 1. This balancing act ensures that for every mole of SO₂ used, one mole of SO₃ is produced, maintaining the mass balance throughout the reaction.

Mole-to-Mass Conversion

Mole-to-mass conversion is an essential skill in chemistry that allows us to relate the number of particles in a substance to its mass. This is achieved by using the substance's molar mass, a constant that gives us the mass of one mole of particles.

For instance, once you've established the molar mass of a compound (like SO₃ with a molar mass of 80.07 g/mol), you can convert moles of that compound to grams by simply multiplying the number of moles by the molar mass. This is what happens in converting the moles of sulfur trioxide produced in a reaction into the mass that can be measured on a balance. If you have 2341.75 mol of SO₃, you would multiply this value by the molar mass of SO₃ to obtain the mass in grams, and, if necessary, convert grams to kilograms. This conversion is the bridge between the molecular scale and the real-world scale where we can observe and measure substances.