Question

Many metals occur naturally as sulfide compounds, examples include \(\mathrm{ZnS}\) and \(\mathrm{CoS}\). Air pollution often accompanies the processing of these ores, because toxic sulfur dioxide is released as the ore is converted from the sulfide to the oxide by roasting (smelting). For example, consider the unbalanced equation for the roasting reaction for zinc: $$ \mathrm{ZnS}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{ZnO}(s)+\mathrm{SO}_{2}(g) $$ How many kilograms of sulfur dioxide are produced when \(1.0 \times 10^{2} \mathrm{~kg}\) of \(\mathrm{ZnS}\) is roasted in excess oxygen by this process?

Short answer

When 100 kg of ZnS is roasted in excess oxygen, 65.7 kg of sulfur dioxide (SO₂) is produced.

Step-by-step solution

1. Balance the chemical equation

To balance the chemical equation, we need to have the same number of each element on both sides of the arrow. In this case, we have one zinc atom, one sulfur atom, and two oxygen atoms on each side. Thus, the balanced equation is: $$ \mathrm{ZnS}(s) + \frac{3}{2}\mathrm{O}_{2}(g) \rightarrow \mathrm{ZnO}(s) + \mathrm{SO}_{2}(g) $$ This indicates that one mole of zinc sulfide reacts with 1.5 moles of oxygen gas to produce one mole of zinc oxide and one mole of sulfur dioxide.

2. Convert the mass of zinc sulfide to moles

To find the moles of zinc sulfide, we need to know its molar mass. The molar mass of ZnS is the sum of the atomic masses of zinc and sulfur: $$ \text{Molar mass of ZnS} = \mathrm{65.38\,g/mol \,(Zn)} + \mathrm{32.07\,g/mol\,(S)} = \mathrm{97.45\,g/mol} $$ Now, we can convert the mass of zinc sulfide to moles: $$ \text{Moles of ZnS} = \frac{\text{Mass of ZnS}}{\text{Molar mass of ZnS}} $$ $$ \text{Moles of ZnS} = \frac{1.0 \times 10^{2}\, \mathrm{kg}}{0.09745\, \mathrm{kg/mol}} = 1.026 \times 10^{3}\, \mathrm{mol} $$

3. Use stoichiometry to find moles of sulfur dioxide produced

From the balanced equation, 1 mole of ZnS reacts to produce 1 mole of SO₂. Therefore, the moles of sulfur dioxide produced will be equal to the moles of zinc sulfide reacted: $$ \text{Moles of SO}_2 = \text{Moles of ZnS} = 1.026 \times 10^3\, \mathrm{mol} $$

4. Convert moles of sulfur dioxide to mass

The molar mass of sulfur dioxide (SO₂) is given by the sum of the atomic masses of sulfur and two oxygen atoms: $$ \text{Molar mass of SO}_2 = \mathrm{32.07\,g/mol\,(S)} + 2 \times \mathrm{16.00\,g/mol\,(O)} = \mathrm{64.07\,g/mol} $$ To find the mass of sulfur dioxide produced, multiply the moles of sulfur dioxide by its molar mass: $$ \text{Mass of SO}_2 = \text{Moles of SO}_2 \times \text{Molar mass of SO}_2 $$ $$ \text{Mass of SO}_2= 1.026 \times 10^3\, \mathrm{mol} \times 0.06407\, \mathrm{kg/mol} = 6.57 \times 10^{1}\, \mathrm{kg} $$ So, when 100 kg of ZnS is roasted in excess oxygen, 65.7 kg of sulfur dioxide (SO₂) is produced.

Key concepts

Stoichiometric Calculations

Stoichiometric calculations are a fundamental aspect of chemistry that deal with determining the relative quantities of reactants and products in chemical reactions. These calculations are based on the balanced chemical equation, which provides the ratio in which reactants combine to form products.

To perform stoichiometric calculations, one typically follows several steps, beginning with writing and balancing the chemical equation. Next, conversion factors known as molar ratios are used, derived from the coefficients of the balanced equation. For instance, if a balanced equation states that 1 mole of substance A reacts with 2 moles of substance B, we can deduce that the molar ratio of A to B is 1:2.

In the context of the educational exercise, after calculating the moles of ZnS, we use stoichiometry to find that the moles of ZnS will equal the moles of SO₂ produced. This straight-forward interpretation of the balanced equation makes stoichiometric calculations a powerful tool in predicting the outcomes of chemical reactions.

Molar Mass

The molar mass of a substance is the weight of one mole of that substance and is expressed in grams per mole (g/mol). It's a critical factor in stoichiometric calculations because it allows us to convert between mass and moles, two different ways of measuring the amount of a substance.

The molar mass is calculated by summing the atomic masses of all the atoms in a molecule. For example, the molar mass of ZnS is found by adding the atomic masses of zinc and sulfur. It's crucial to always ensure the accuracy of these values, as they are essential for reliable stoichiometric calculations.

Practical Application of Molar Mass

For a practical application, consider a situation where you're given the mass of ZnS in kilograms and need to find the amount of SO₂ produced in a reaction. By converting kilograms to grams, you can use the molar mass of ZnS to find the moles of ZnS, which is crucial for further stoichiometric calculations.

Chemical Reactions

Chemical reactions are processes where reactants transform into products through the rearrangement of atoms. They are described by chemical equations, which indicate the substances involved and their relative proportions.

An important characteristic of chemical reactions is the conservation of mass, stating that matter cannot be created or destroyed within a closed system. This principle is reflected in the fact that the total mass of the reactants equals the total mass of the products.

Types of Chemical Reactions

There are various types of chemical reactions including synthesis, decomposition, single replacement, and double replacement. The roasting of ZnS to form ZnO and SO₂, as mentioned in the exercise, is an example of a chemical reaction where a single substance is decomposed into two different products.

Balancing Equations

Balancing equations is crucial for stoichiometry as it ensures that the law of conservation of mass is satisfied – meaning the number of atoms of each element is the same on both sides of the reaction. This is achieved by adjusting the coefficients in front of the compounds in the reaction.

For example, in the equation for roasting zinc sulfide, the initial unbalanced equation does not reflect an equal number of each element on both sides. Upon balancing, we find that 1 mole of ZnS will react with 1.5 moles of O₂ to produce 1 mole each of ZnO and SO₂.

Tricks for Balancing Equations

When dealing with fractions as coefficients, like the 1.5 moles of O₂, it's often helpful to double all coefficients to eliminate the fraction. This would lead to a balanced equation with whole number coefficients, which is typically preferred for clarity.