Problem 97 - General Chemistry: Principles and Modern Applications

Question

When \(10.0 \mathrm{g}\) zinc and \(8.0 \mathrm{g}\) sulfur are allowed to react, all the zinc is consumed, \(14.9 \mathrm{g}\) zinc sulfide is produced, and the mass of unreacted sulfur remaining is (a) \(2.0 \mathrm{g}\) (b) \(3.1 g\) (c) \(4.9 \mathrm{g}\) (d) impossible to predict from this information alone

Step-by-Step Solution

Answer

The mass of the unreacted sulfur remaining is \(3.1 \mathrm{g}\).

Step 1: Identify the mass of the initial reactants

The mass of the initial reactants are given in the problem statement: 10.0g zinc and 8.0g sulfur. So total mass of the initial reactants is \(10.0 \mathrm{g} + 8.0 \mathrm{g} = 18.0 \mathrm{g}\).

Step 2: Calculate the mass of the zinc sulfide produced

All the zinc is consumed and 14.9g of zinc sulfide is produced. This gives us the total mass of the reaction products.

Step 3: Find the mass of the unreacted sulfur

The mass of unreacted sulfur can be found by subtracting the mass of the zinc sulfide produced from the total mass of the initial reactants. That is \(18.0 \mathrm{g} - 14.9 \mathrm{g} = 3.1 \mathrm{g}\). Thus the remaining mass of sulfur is 3.1g.

Key Concepts

Zinc Sulfide Formation

Zinc sulfide forms when zinc and sulfur undergo a chemical reaction. When these two elements are combined, they create a compound known as zinc sulfide \( ext{(ZnS)}\).In this instance, the reaction can be represented by the balanced chemical equation:\[\text{Zn} + \text{S} \rightarrow \text{ZnS}\]This equation shows that one atom of zinc reacts with one atom of sulfur to produce one unit of zinc sulfide.
Zinc (Zn) and sulfur (S) are joined together by ionic bonds, which are formed when one atom donates electrons to another atom. This reaction is exothermic, meaning it releases energy in the form of heat. It is very efficient, as all the zinc is converted into zinc sulfide while some sulfur may remain unreacted.

• Zinc sulfide is a white crystalline solid.
• It is often used in optical materials and luminescent applications.

Limiting Reactant

A limiting reactant is the reactant in a chemical reaction that is entirely consumed first, limiting the amount of product formed.
In the reaction between zinc and sulfur, zinc is the limiting reactant. This means that once all the zinc is used up, the reaction stops, even if there is more sulfur available.To determine which reactant is the limiting one, we must consider the molar amounts of each reactant:

• Molar mass of zinc (Zn): \(65.38 \ g/mol\)
• Molar mass of sulfur (S): \(32.07 \ g/mol\)

Given 10.0 g of zinc and 8.0 g of sulfur:- Moles of zinc = \(\frac{10.0 \ g}{65.38 \ g/mol} \approx 0.153 \ mol\)- Moles of sulfur = \(\frac{8.0 \ g}{32.07 \ g/mol} \approx 0.249 \ mol\)Since zinc has fewer moles than sulfur, zinc is the limiting reactant, determining the maximum amount of zinc sulfide that can be formed.

Chemical Reaction Mass Balance

Chemical reaction mass balance assures that the total mass of reactants equals the total mass of products.
This is a fundamental principle governed by the law of conservation of mass.In this reaction:- Total mass of reactants = \(10.0 \ \text{g (Zn)} + 8.0 \ \text{g (S)} = 18.0 \ \text{g}\)- Mass of zinc sulfide produced = 14.9 g- Total mass of products = Mass of zinc sulfide + Mass of unreacted sulfur = \(14.9 \ \text{g} + 3.1 \ \text{g} = 18.0 \ \text{g}\)As demonstrated, the sum of the masses of zinc sulfide and unreacted sulfur perfectly matches the initial total mass of the reactants, upholding the principle of mass conservation.This concept ensures that calculations related to chemical reactions are valid and reliable, especially in answering questions involving leftover quantities of reactants and ensuring no mass discrepancy.