Problem 7 - Chemistry and Chemical Reactivity

Question

The metals industry was a major source of air pollution years ago. One common process involved "roasting" metal sulfides in the air: $$2 \mathrm{PbS}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{PbO}(\mathrm{s})+2 \mathrm{SO}_{2}(\mathrm{g})$$ If 2.50 mol of \(\mathrm{PbS}\) is heated in air, what amount of \(\mathrm{O}_{2}\) is required for complete reaction? What amounts of \(\mathrm{PbO}\) and \(\mathrm{SO}_{2}\) are expected?

Step-by-Step Solution

Answer

3.75 mol of \(\mathrm{O}_{2}\), 2.50 mol of \(\mathrm{PbO}\), and 2.50 mol of \(\mathrm{SO}_{2}\).

Step 1: Identify the Balanced Equation

The balanced chemical equation for the reaction is given as:\[ 2 \mathrm{PbS}(\mathrm{s}) + 3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{PbO}(\mathrm{s}) + 2 \mathrm{SO}_{2}(\mathrm{g}) \] This means that 2 moles of \(\mathrm{PbS}\) react with 3 moles of \(\mathrm{O}_{2}\) to produce 2 moles of \(\mathrm{PbO}\) and 2 moles of \(\mathrm{SO}_{2}\).

Step 2: Calculate Moles of O2 Required

According to the balanced equation, for every 2 moles of \(\mathrm{PbS}\), 3 moles of \(\mathrm{O}_{2}\) are required. Set up a ratio to find the moles of \(\mathrm{O}_{2}\) needed for 2.50 moles of \(\mathrm{PbS}\):\[ \frac{3 \text{ moles } \mathrm{O}_{2}}{2 \text{ moles } \mathrm{PbS}} = \frac{x \text{ moles } \mathrm{O}_{2}}{2.50 \text{ moles } \mathrm{PbS}} \]Solve for \(x\), which equals the moles of \(\mathrm{O}_{2}\) required:\[ x = \frac{3}{2} \times 2.50 = 3.75 \text{ moles } \mathrm{O}_{2} \]

Step 3: Calculate Moles of PbO Produced

The reaction shows that 2 moles of \(\mathrm{PbS}\) yield 2 moles of \(\mathrm{PbO}\). Therefore, the amount of \(\mathrm{PbO}\) produced will be the same as the amount of \(\mathrm{PbS}\) used, which is 2.50 moles. Thus, 2.50 moles of \(\mathrm{PbO}\) are produced.

Step 4: Calculate Moles of SO2 Produced

Similarly to \(\mathrm{PbO}\), 2 moles of \(\mathrm{PbS}\) produce 2 moles of \(\mathrm{SO}_{2}\). Therefore, the moles of \(\mathrm{SO}_{2}\) produced from 2.50 moles of \(\mathrm{PbS}\) is also 2.50 moles.

Key Concepts

Balanced Chemical Equation

In any chemical reaction, a balanced chemical equation is essential. It acts like a map, showing you how molecules come together to form new substances. A balanced equation ensures that the same number of each type of atom appears on both the reactant and product sides of the equation. In chemistry, this is crucial for obeying the Law of Conservation of Mass, which states that mass cannot be created or destroyed during a chemical reaction.

Let’s take the chemical reaction you're working with as an example: \[ 2 \mathrm{PbS}(\mathrm{s}) + 3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{PbO}(\mathrm{s}) + 2 \mathrm{SO}_{2}(\mathrm{g}) \]
This means every 2 moles of lead(II) sulfide (\(\mathrm{PbS}\)) requires 3 moles of oxygen gas (\(\mathrm{O}_2\)) to produce 2 moles each of lead(II) oxide (\(\mathrm{PbO}\)) and sulfur dioxide (\(\mathrm{SO}_2\)). The coefficients (2, 3, 2, 2) in front of each molecule are key in balancing the equation.

Why does this matter? Balanced equations are fundamental for performing calculations like figuring out reactants' and products' amounts. Without them, any calculations on the substances involved would result in the wrong amounts.

Moles Calculation

Moles are a central concept in chemistry, helping us count how much of a substance is involved in a reaction. The mole is a bridge between the atomic world and the real world, allowing us to weigh out practical amounts of chemicals based on atomic scale numbers.

When dealing with moles, it's all about proportions. In the original exercise, we calculated the moles of oxygen (\(\mathrm{O}_2\)) needed by using the balanced chemical equation. If we know the moles of \(\mathrm{PbS}\), we can use the equation to find out the required moles of \(\mathrm{O}_2\). Here's how:

• We have the ratio from the balanced equation: 2 moles of \(\mathrm{PbS}\) react with 3 moles of \(\mathrm{O}_2\).
• We start with 2.50 moles of \(\mathrm{PbS}\). Use the ratio to solve for moles of \(\mathrm{O}_2\):

\[\frac{3 \text{ moles } \mathrm{O}_2}{2 \text{ moles } \mathrm{PbS}} = \frac{x \text{ moles } \mathrm{O}_2}{2.50 \text{ moles } \mathrm{PbS}}\] Solving for \(x\) gives us 3.75 moles of \(\mathrm{O}_2\) required. This kind of calculation helps chemists determine precise amounts of chemicals needed for reactions, ensuring everything reacts completely without leftovers.

Chemical Reactions

Chemical reactions are dynamic processes where substances, known as reactants, transform into new substances called products. This transformation involves breaking old bonds and forming new ones, leading to changes in molecular structures. In the context of your exercise, the reaction is a classic example of a redox reaction, involving the roasting of metal sulfides in air.

Reactants \(\mathrm{PbS}(\mathrm{s})\) and \(\mathrm{O}_2(\mathrm{g})\) undergo a reaction where bonds in \(\mathrm{PbS}\) and \(\mathrm{O}_2\) are broken. The creation of new bonds results in products \(\mathrm{PbO}(\mathrm{s})\) and \(\mathrm{SO}_2(\mathrm{g})\).

• The reaction highlights how an element, sulfur, is oxidized while helping lead form an oxide.
• This type of reaction is significant in understanding industrial processes, especially those contributing to pollution.

Understanding these reactions allows us to make informed choices and devise strategies in related fields like pollution control and resource management. Chemical reactions like this one play an essential role in industries, explaining why correct stoichiometry is vital for efficiency and environmental considerations.