Question

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

Short answer

The theoretical yields for each case are: (a) 5.33 g AlCl3, (b) 20.0 g AlCl3, (c) 0.703 g AlCl3.

Step-by-step solution

Calculate the Molar Mass of Reactants and Product

First, calculate the molar mass of aluminum (Al), which is 26.98 g/mol, and chlorine (Cl2), 70.90 g/mol (since Cl has an atomic mass of 35.45 and there are two Cl atoms in Cl2). The molar mass of aluminum chloride (AlCl3) is 133.34 g/mol (1 Al atom at 26.98 g/mol + 3 Cl atoms at 35.45 g/mol each).

Convert Grams to Moles for Each Reactant

Using the molar mass, convert each given mass of reactants into moles. Moles of Al = mass of Al (in g) / molar mass of Al (in g/mol). Moles of Cl2 = mass of Cl2 (in g) / molar mass of Cl2 (in g/mol).

Determine the Limiting Reactant

Use the stoichiometry of the reaction (2 moles of Al react with 3 moles of Cl2 to produce 2 moles of AlCl3) to find out which reactant will be completely consumed first - the limiting reactant - for each set of reactants (a, b, c).

Calculate Theoretical Yield of AlCl3

Using the number of moles of the limiting reactant, calculate the theoretical yield in moles of AlCl3 based on the balanced equation. Then convert the moles of AlCl3 to grams using its molar mass.

Perform Calculations for Each Initial Amount of Reactants

Perform the above steps separately for each case (a, b, c) to obtain the theoretical yield in grams for each.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. For a chemical equation to be stoichiometrically balanced, the number of atoms of each element must be the same on both the reactant and product sides of the equation.

For instance, in the reaction between aluminum (Al) and chlorine gas (Cl₂) to produce aluminum chloride (AlCl₃), the stoichiometric coefficients are as follows: 2 moles of Al react with 3 moles of Cl₂ to produce 2 moles of AlCl₃. These coefficients are crucial as they indicate the proportions at which the substances react. Understanding these proportions allows us to predict the amounts of reactants required and the amounts of products that will be formed.

Molar Mass

The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It plays an essential role in stoichiometry because it allows us to convert between mass in grams and the number of moles, which is a count of particles.

In our example, the molar masses calculated were 26.98 g/mol for aluminum, 70.90 g/mol for chlorine gas, and 133.34 g/mol for aluminum chloride. These molar masses are derived from the atomic masses of the individual elements found on the periodic table. By knowing the molar mass, you can convert the mass of a substance provided in grams to moles, which can then be used in stoichiometric calculations to predict how much product can form from given reactant amounts.

Limiting Reactant

The limiting reactant in a chemical reaction is the reactant that will be completely consumed first, limiting the amount of product that can be formed. It is essential to identify the limiting reactant to accurately calculate the theoretical yield of a reaction.

In our reaction, the limiting reactant is determined by comparing the mole ratio of the available reactants to the mole ratio of the balanced equation. For the reactants given in the problem, this involves calculating the moles of Al and Cl₂ and then finding which one would run out first if the reaction proceeded according to the stoichiometric coefficients from the balanced equation. The one that runs out first is the limiting reactant, and all subsequent calculations for the theoretical yield are based on its amount.

Chemical Reaction Quantification

Quantifying a chemical reaction involves using stoichiometric principles to calculate the amounts of reactants and products involved in the reaction. The theoretical yield is the amount of product that would be formed if the reaction proceeded perfectly and all of the limiting reactant was converted into product with no losses.

After determining the limiting reactant, you can calculate the theoretical yield by using the stoichiometry of the reaction. For instance, if the limiting reactant can produce a certain number of moles of product according to the balanced equation, you can then multiply this by the molar mass of the product to find the theoretical yield in grams. These calculations allow chemists to predict how much product can be obtained and are fundamental in both laboratory work and industrial processes.