Problem 24 - Chemistry The Molecular Nature of Matter

Question

A mixture of \(0.020 \mathrm{~mol}\) of \(\mathrm{Mg}\) and \(0.020 \mathrm{~mol}\) of \(\mathrm{Cl}_{2}\) reacted completely to form \(\mathrm{MgCl}_{2}\) according to the equation $$ \mathrm{Mg}+\mathrm{Cl}_{2} \longrightarrow \mathrm{MgCl}_{2} $$ What information describes the stoichiometry of this reaction? What information gives the scale of the reaction?

Step-by-Step Solution

Answer

The stoichiometry is described by the 1:1:1 ratio of Mg:Cl2:MgCl2 in the balanced chemical equation. The scale of the reaction is described by the amounts of reactants used, which is 0.020 mol of Mg and 0.020 mol of Cl2.

Step 1: Identifying the Stoichiometry of the Reaction

Examine the balanced chemical equation \(\mathrm{Mg} + \mathrm{Cl}_{2} \longrightarrow \mathrm{MgCl}_{2}\) to determine the stoichiometry. In this equation, 1 mole of magnesium (\mathrm{Mg}) reacts with 1 mole of chlorine gas (\mathrm{Cl}_{2}) to produce 1 mole of magnesium chloride (\mathrm{MgCl}_{2}). The stoichiometric coefficients are all 1.

Step 2: Determining the Scale of the Reaction

The scale of the reaction is provided by the actual quantities of the reactants that took part in the reaction. Here, it is given that \(0.020\ \mathrm{mol}\) of \(\mathrm{Mg}\) and \(0.020\ \mathrm{mol}\) of \(\mathrm{Cl}_{2}\) reacted. So, the scale of the reaction is \(0.020\ \mathrm{mole}\) for each reactant.

Key Concepts

Chemical Reaction Equation

Understanding the chemical reaction equation is fundamental in studying chemistry and stoichiometry. It serves as a recipe, outlining exactly what reactants are needed and what products will form. For instance, the equation \[\mathrm{Mg} + \mathrm{Cl}_{2} \longrightarrow \mathrm{MgCl}_{2}\]illustrates the reaction between magnesium \(\mathrm{Mg}\) and chlorine gas \(\mathrm{Cl}_{2}\) to produce magnesium chloride \(\mathrm{MgCl}_{2}\). This particular equation indicates that one atom of magnesium reacts with one molecule of chlorine gas to yield one formula unit of magnesium chloride. Science makes a big deal about these equations because they tell us the proportion in which substances react and form, which is the heart of stoichiometry.

While the equation looks simple, each component—reactants and products—is governed by the law of conservation of mass, meaning the total mass of the reactants must equal the total mass of the products. That's why balancing the equation is so critical. Properly balanced, it ensures that the number of atoms for each element is the same on both sides of the reaction, hence sticking to the rules of conservation.

When working with a chemical equation, always check to make sure it's balanced. It provides a clear picture of the reaction and is a necessary step before performing any stoichiometric calculations.

Mol Ratio

The mol ratio is an essential concept in stoichiometry that refers to the proportions of reactants and products in a chemical reaction. In the given equation \[\mathrm{Mg} + \mathrm{Cl}_{2} \longrightarrow \mathrm{MgCl}_{2}\],the coefficients of the reactants and the product are all '1'. This straightforwardly suggests a 1:1:1 mol ratio, indicating that one mole of magnesium reacts with one mole of chlorine gas to produce one mole of magnesium chloride.

This ratio is powerful; it allows chemists to predict how much product can be formed from a given amount of reactant and vice versa. To utilize the mol ratio effectively, students should understand the following:

• One mole of any substance contains the same number of entities (atoms, molecules, formula units, etc.)—Avogadro's number, which is approximately \(6.022 \times 10^{23}\).
• The mol ratio can be applied across different scales of a chemical reaction, from the laboratory to industrial processes, as long as we're dealing with proportional amounts.
• It is derived directly from the balanced chemical equation and is essential in making calculations such as determining limiting reactants, theoretical yields, and percent yields.

Understanding the mol ratio, therefore, not only allows for quantitative analysis of chemical reactions but also provides a bridge between the microscopic scale of atoms and molecules and the macroscopic world of grams and liters.

Reaction Scale

The reaction scale describes the quantity of reactants and products involved in a chemical reaction. While the stoichiometry tells us the 'what' and 'how much' in terms of mole ratios, the reaction scale tells us the 'how much' in practical, real-world amounts. For example, the scale of the reaction in our exercise can be understood in terms of how much reactant we started with: \(0.020\ mathrm{mol}\) of each \(mathrm{Mg}\) and \(mathrm{Cl}_{2}\).

This scale helps translate the theoretical aspect of stoichiometry into relatable quantities that can be measured and used in lab settings. Here’s what’s key about the reaction scale:

• It represents the actual amount of substances used in a reaction as given or found in a lab or industry, rather than the idealized ratios in the balanced equation.
• The scale can vary significantly—from millimoles in a research lab to kilomoles in industrial-scale chemistry—but the underlying stoichiometric relationships remain constant.
• By knowing the scale, chemists can calculate the practical yield of a reaction, determine reactant masses, and predict the amount of product formed.

In teaching stoichiometry, emphasizing the concept of reaction scale can really help students to visualize the process and its practical outcomes. It takes the abstract nature of chemical equations and anchors them in the tangible world.