Question

For the reaction shown, calculate the theoretical yield of product (in grams) for each initial amount of reactants. $$ 2 \mathrm{Al}(s)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AlCl}_{3}(s) $$ a. \(2.0 \mathrm{~g} \mathrm{Al}, 2.0 \mathrm{~g} \mathrm{Cl}_{2}\) b. \(7.5 \mathrm{~g} \mathrm{Al}, 24.8 \mathrm{~g} \mathrm{Cl}_{2}\) c. \(0.235 \mathrm{~g} \mathrm{Al}, 1.15 \mathrm{~g} \mathrm{Cl}_{2}\)

Short answer

The theoretical yield of AlCl3 for each set of reactants is: a) 2.89 g, b) 20.1 g, c) 0.325 g. Calculations are based on limiting reactant for each scenario and stoichiometry of the balanced chemical equation.

Step-by-step solution

Calculate the molar mass of reactants and product

Find the molar masses by using the periodic table: Molar mass of Al is 26.98 g/mol and Cl2 is 70.90 g/mol. Molar mass of AlCl3 is 133.34 g/mol (26.98 g/mol for Al + 3 × 35.45 g/mol for Cl).

Determine the moles of reactants

Use the molar mass to convert the mass of each reactant to moles: Moles of Al = mass of Al (g) ÷ molar mass of Al (g/mol); Moles of Cl2 = mass of Cl2 (g) ÷ molar mass of Cl2 (g/mol).

Identify the limiting reactant

The limiting reactant is the reactant that will be consumed first, thereby limiting the amount of product that can be formed. Use the stoichiometry of the reaction (2 mol Al : 3 mol Cl2) to find the limiting reactant for each set of masses given.

Calculate the moles of product from the limiting reactant

Use the stoichiometric ratio from the balanced equation to convert moles of the limiting reactant to moles of product (1 mol AlCl3 forms from 1 mol Al or 3 mol Cl2).

Calculate the theoretical yield in grams

Multiply the moles of product by the molar mass of the product to find the theoretical yield in grams.

Repeat calculation for each initial amount of reactants

Perform steps 2 to 5 for each given set of reactant masses (a, b, and c).

Key concepts

Stoichiometry

Stoichiometry is like a recipe for chemistry, but instead of measuring ingredients for cooking, we measure the amounts of substances involved in chemical reactions. Understanding stoichiometry means knowing how much of each substance is needed to react completely and how much product we can expect at the end.

For chemical reactions, each element has a molar mass, which is used to convert between grams and moles, a key step in stoichiometry. In the given exercise, the balanced chemical equation shows us the exact ratio of reactants (aluminum and chlorine) that react to form the product (aluminum chloride).

Here’s why stoichiometry is important: If we start with a different amount of each reactant, the stoichiometry tells us which reactant will run out first and stop the reaction. This concept leads us to find the 'limiting reactant', which determines the theoretical yield of the product.

Limiting Reactant

The limiting reactant is essentially the 'bottleneck' of a chemical reaction—the ingredient that runs out first and thus limits the amount of product that can be formed. It’s like when you run out of flour while baking cookies; no matter how much of the other ingredients you have, you’re stuck!

Using our stoichiometric calculations, we compare the mole ratio of the reactants to their ratio in the balanced equation, which then tells us which reactant limits the reaction. In the solution steps, we find the limiting reactant by determining which reactant would produce the least amount of product if all of it were used up. Once identified, this reactant dictates the maximum amount of product we can get, known as the theoretical yield.

Molar Mass

Molar mass is a key player in stoichiometry—the bridge between the mass of a substance and the number of moles. Think of it as the 'weight' of one mole of a substance. The molar mass of an element can be found on the periodic table, typically in units of grams per mole (g/mol). For a compound, like aluminum chloride in our exercise, we add up the molar masses of all the atoms in the molecule.

To calculate this, multiply the number of each type of atom by its respective molar mass from the periodic table and sum it all up. For example, in AlCl₃, we have one aluminum atom and three chlorine atoms, so its molar mass is the sum of one Al molar mass and three times the Cl molar mass. This step is crucial for converting the reactants' mass in grams to the amount in moles, setting the stage for finding the limiting reactant.

Chemical Reaction

A chemical reaction is a process where substances, called reactants, transform into different substances, called products. It's like a magical transformation where substances rearrange their atoms to form new ones. Our equation, \(2 \text{Al}(s) + 3 \text{Cl}_2(g) \rightarrow 2 \text{AlCl}_3(s)\), is a perfect example of a chemical reaction where solid aluminum reacts with chlorine gas to produce solid aluminum chloride.

The equation is balanced, meaning there are equal numbers of each type of atom on both sides of the reaction. This balance is the basis of stoichiometry and necessary for all subsequent calculations, including identifying the limiting reactant and determining the theoretical yield. In essence, knowing how substances interact in a chemical reaction allows us to predict the products and their amounts, connecting the concepts of stoichiometry, limiting reactant, and molar mass within the realm of chemical reactions.