Question

Zinc sulfide reacts with oxygen according to the reaction: $$2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g) $$ A reaction mixture initially contains 4.2 \(\mathrm{mol} \mathrm{ZnS}\) and 6.8 \(\mathrm{mol} \mathrm{O}_{2}\) . Once the reaction has occurred as completely as possible, what amount (in moles) of the excess reactant remains?

Short answer

0.5 moles of O2 remain as the excess reactant.

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation for the reaction between zinc sulfide and oxygen is already given: \[2 \mathrm{ZnS}(s) + 3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s) + 2 \mathrm{SO}_{2}(g)\]It shows that 2 moles of ZnS react with 3 moles of O2 to produce 2 moles of ZnO and 2 moles of SO2.

Determine the limiting reactant

To find the limiting reactant, use the initial amounts of ZnS and O2 and the stoichiometry of the balanced equation. From the equation, the stoichiometric ratio of ZnS to O2 is 2:3. Calculate the amount of O2 needed to completely react with 4.2 moles of ZnS using the ratio.\[\left(\frac{3 \text{ moles of } O_2}{2 \text{ moles of } ZnS}\right) \times 4.2 \text{ moles of ZnS} = 6.3 \text{ moles of O2 needed} \]Since there are 6.8 moles of O2 available, which is more than the 6.3 moles needed, ZnS is the limiting reactant.

Calculate the moles of excess reactant remaining

Subtract the amount of O2 that actually reacted (which is the amount needed) from the initial amount of O2.\[6.8 \text{ moles initial O2} - 6.3 \text{ moles O2 reacted} = 0.5 \text{ moles O2 remaining}\]0.5 moles of O2 are left over after the reaction has gone to completion.

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships that govern a chemical reaction. It is essentially about calculating the proportions of elements and compounds involved in chemical reactions. At the heart of stoichiometry is the balanced chemical equation, which provides the mole ratios of reactants and products – pivotal in determining how much of each substance is needed or produced.

In the exercise given, the stoichiometry between zinc sulfide (ZnS) and oxygen (O2) follows the ratio given by the coefficients in the balanced chemical equation: for every 2 moles of ZnS, 3 moles of O2 are required. Understanding these ratios is crucial because it allows us to predict the outcome of the reaction in terms of which reactant will be used up first (the limiting reactant) and how much of the other reactants will be left over (the excess reactants).

For example, in applications beyond the classroom, such calculations are necessary for scaling reactions for industrial purposes, where cost efficiency and safety are of primary concern.

Chemical Reaction Balancing

Balancing chemical equations is an essential skill in chemistry because it ensures that the law of conservation of mass is upheld in a chemical reaction. According to this law, mass cannot be created or destroyed in a chemical reaction, which means the mass of the reactants must equal the mass of the products.

In the exercise, the initial chemical equation is already balanced for us: \[2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g) \]Each element on the left-hand side (reactants) appears in the same quantity on the right-hand side (products). Balancing an equation involves adjusting coefficients, the numbers in front of compounds, to achieve this equality. Balancing chemical equations allows us to accurately use stoichiometry to calculate reactants and products forming the basis for subsequent calculations, such as finding the limiting reactant.

Mole Concept

The mole concept is a fundamental cornerstone of chemistry because it provides a bridge between the atomic or molecular scale and the macroscopic world we observe. A mole is a unit that represents a very large quantity of entities, typically atoms or molecules, and is defined as exactly 6.022 x 10²³ entities, which is Avogadro's number.

In stoichiometric calculations, we use the mole unit to quantify substances because the mass alone would not tell us the number of molecules or atoms involved. The exercise demonstrates the use of the mole concept through the calculation involving the reaction mixture of ZnS and O2. The mole allows us to use the balanced equation to predict the amounts of products formed from certain amounts of reactants and to recognize that moles of ZnS will completely react with moles of O2 based on the mole ratio (stoichiometry) from the balanced equation. The understanding of the mole concept is not only vital for classroom exercises but also for practical laboratory work and industrial chemistry applications.