Mastering Stoichiometry: A Step-by-Step Guide

Stoichiometry is a fundamental concept in chemistry that helps us understand the quantitative relationships between reactants and products in chemical reactions. This guide will walk you through the process of solving a stoichiometry problem using the given balanced equation and dimensional analysis.

Understanding the Balanced Equation

The given balanced equation is: 2 ZnS 3O2 → 2 ZnO 2 SO2. This equation tells us that 2 moles of zinc sulfide (ZnS) react with 3 moles of oxygen (O2) to produce 2 moles of zinc oxide (ZnO) and 2 moles of sulfur dioxide (SO2).

Given Problem: ZnS to SO2

We need to find the volume of SO2 produced from 9.7 g of ZnS. Let's break down the steps to get the solution.

Step 1: Identify Start and End Points

We start with the mass (9.7 g) of ZnS and need to find the volume of SO2. Our goal is to transform the units from grams of ZnS to liters of SO2 using dimensional analysis.

Step 2: Gather Conversion Factors

To solve this problem, we need to convert grams to moles, then use the stoichiometric relationship to find the moles of SO2, and finally convert moles to volume using the ideal gas law.

Step 2.1: Convert grams of ZnS to moles

The molecular weight (m.w.) of ZnS is 97.474 g/mol.

Math: (frac{9.7, text{g ZnS}}{97.474, text{g/mol ZnS}} 0.10 , text{moles ZnS})

Step 2.2: Use the Chemical Equation to Find Moles of SO2

From the balanced equation: 2 moles ZnS produce 2 moles SO2.

Therefore, 0.1 moles ZnS will produce 0.1 moles SO2.

Step 2.3: Use the Ideal Gas Law to Find Volume of SO2

The ideal gas law is: (PV nRT).

Rearranging to find volume (V frac{nRT}{P}).

Plugging in the values: (V frac{0.1 , text{moles} times 0.0821 , text{L} cdot text{atm} cdot text{K}^{-1} cdot text{mol}^{-1} times 298 , text{K}}{1 , text{atm}} 2.41 , text{L}).

Step 3: Convert the Result to Cubic Decimeters

Since 1 liter (L) 1 cubic decimeter (dm3), the volume of SO2 is 2.41 dm3.

The nearest multiple-choice answer is 2.4 dm3

General Process for Stoichiometry Problems

Whenever you encounter a stoichiometry or dimensional analysis problem, follow these steps:

Identify what you know and where you want to go.

Gather all the necessary conversion factors.

Make the units work by setting up the correct fractions to cancel out the unwanted units.

Perform the calculations and verify that the final units match the desired output.

Make sure to use the known values like molecular weights, ideal gas law constants, and standard conditions (e.g., 25°C and 1 atm).

Conclusion

By following these steps, you can solve any stoichiometry problem without memorizing a complicated list of steps. The key is to understand the fundamental relationships between reactants and products and use dimensional analysis to guide your calculations.

Feel free to comment with any questions or to share your thoughts. Let's continue to explore more chemistry concepts together!