Smelting of ores to produce pure metals is an atmospheric source of sulfur dioxide. (a) Galena, the most common mineral of lead, is primarily lead(II) sulfide (PbS). The first step in the production of pure lead is to oxidize lead sulfide into lead(II) sulfite (PbSO3). Lead(II) sulfite is then thermally decomposed into lead(II) oxide and sulfur dioxide gas. Balance the following equation: PbSO3 (s) → heat → PbO (s) + SO2 (g). (b) How many liters of SO2 are produced at 1 atm and 300 °C if 250 g of PbSO3 is decomposed?

Verified step by step guidance

1. Step 1: Begin by balancing the chemical equation for the decomposition of lead(II) sulfite (PbSO3) into lead(II) oxide (PbO) and sulfur dioxide (SO2). Since there is one Pb atom, one S atom, and three O atoms on both sides of the equation, the equation is already balanced: PbSO3 (s) → PbO (s) + SO2 (g).
2. Step 2: Calculate the molar mass of PbSO3. Use the periodic table to find the atomic masses: Pb = 207.2 g/mol, S = 32.07 g/mol, and O = 16.00 g/mol. Add these to find the molar mass of PbSO3.
3. Step 3: Convert the mass of PbSO3 (250 g) to moles using its molar mass. Use the formula: moles = mass (g) / molar mass (g/mol).
4. Step 4: Use the stoichiometry of the balanced equation to determine the moles of SO2 produced. According to the balanced equation, 1 mole of PbSO3 produces 1 mole of SO2.
5. Step 5: Use the ideal gas law to calculate the volume of SO2 produced at 1 atm and 300 °C. First, convert the temperature to Kelvin by adding 273.15 to the Celsius temperature. Then, use the ideal gas law: PV = nRT, where P is pressure, V is volume, n is moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is temperature in Kelvin. Solve for V.

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is essential in stoichiometry, ensuring that the number of atoms for each element is the same on both sides of the equation. This reflects the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. In the given reaction, balancing involves adjusting coefficients to achieve this equality, which is crucial for accurate calculations of reactants and products.

Thermal Decomposition

Thermal decomposition is a chemical reaction where a compound breaks down into simpler substances when heated. In this case, lead(II) sulfite (PbSO3) decomposes into lead(II) oxide (PbO) and sulfur dioxide (SO2) upon heating. Understanding this process is vital for predicting the products of the reaction and the conditions required for the reaction to occur.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is fundamental for calculating the volume of gases produced in reactions, such as the sulfur dioxide generated from the decomposition of PbSO3. By knowing the amount of substance and the conditions (pressure and temperature), one can determine the volume of gas produced using this equation.