Question

The balanced equation for the reaction of aluminum metal and chlorine gas is $$ 2 \mathrm{Al}(s)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AlCl}_{3}(s) $$ Assume that \(0.40 \mathrm{~g} \mathrm{Al}\) is mixed with \(0.60 \mathrm{~g} \mathrm{Cl}_{2}\). (a) What is the limiting reactant? (b) What is the maximum amount of \(\mathrm{AlCl}_{2}\), in grams, that can be produced?

Short answer

The limiting reactant is Cl2 and the maximum amount of AlCl3 that can be produced is 0.76 g.

Step-by-step solution

Determine the amount (in moles) of Aluminum and Chlorine

First, we need to convert the mass of Aluminum and Chlorine to moles. This is done using the molar masses of Aluminum and Chlorine. The molar mass of Aluminum is approximately 26.98 g/mol and the molar mass of Cl2 is approximately 70.90 g/mol. So, the amount of Aluminum in moles = \(0.40 \ g \ / \ 26.98 \ g/mol = 0.0148 \ mol\) and the amount of Chlorine in moles = \(0.60 \ g \ / \ 70.90 \ g/mol = 0.0085 \ mol\)

Identify the limiting reactant

The reactant that produces the least amount of product is the limiting reactant. According to the balanced chemical equation, 2 moles of Al reacts with 3 moles of Cl2. Therefore, we can calculate the amount of AlCl3 formed by each reactant: Al can produce \(0.0148 \ mol \ Al \times \ (2 \ mol \ AlCl3 \ / \ 2 \ mol \ Al) = 0.0148 \ mol \ AlCl3\), and Cl2 can produce \(0.0085 \ mol \ Cl2 \times \ (2 \ mol \ AlCl3 \ / \ 3 \ mol \ Cl2) = 0.0057 \ mol \ AlCl3\). Because Cl2 produces less AlCl3, it is limiting reactant.

Calculate the maximum amount of AlCl3 that can be produced

The amount of product formed is determined by the limiting reactant. Hence, we use the amount of Cl2 to calculate the mass of AlCl3. Since Cl2 forms 0.0057 moles of AlCl3, and the molar mass of AlCl3 is approximately 133.34 g/mol, the maximum amount of AlCl3 that can be produced = \(0.0057 \ mol \× \ 133.34 \ g/mol = 0.76 \ g\)

Key concepts

Limiting Reactant

Understanding the concept of the limiting reactant is crucial in chemical reaction stoichiometry. It refers to the reactant that will be completely consumed first during a chemical reaction, thus determining the amount of product that can be formed. This is because once the limiting reactant is used up, the reaction stops, and no additional product can be created, regardless of how much of the other reactants remains.

In our example, when aluminum (Al) reacts with chlorine gas (Cl₂), we must compare the mole ratios in which these reactants combine, according to the balanced equation. The calculation shows that chlorine is the limiting reactant because it produces a smaller amount of the desired product aluminum chloride (AlCl₃). Consequently, chlorine dictates the maximum amount of AlCl₃ that can be synthesized from the given reactants.

Mole-to-Mole Ratio

The mole-to-mole ratio is derived from the coefficients of a balanced chemical equation and indicates the proportions in which reactants combine and products form. It essentially serves as a conversion factor between moles of different substances in a reaction.

In the given reaction of aluminum and chlorine, the mole-to-mole ratio between aluminum and aluminum chloride is 1:1, and between chlorine and aluminum chloride is 3:2, as indicated by the balanced equation coefficients. These ratios are key to determining the amounts of reactants needed for a complete reaction and for calculating the theoretical yield of the product.

Using these ratios, we deduced that chlorine was the limiting reactant and then used the ratio to calculate the maximum amount of AlCl₃ that could be produced in our exercise.

Molar Mass

The molar mass is a fundamental property of a substance, defined as the mass of one mole of that substance, typically expressed in grams per mole (g/mol). It's determined by summing up the atomic masses of all the atoms in the molecular formula. The molar mass is vital for converting between the mass of a substance and the amount of substance in moles.

In stoichiometry problems like our example, we calculate the number of moles of aluminum and chlorine by dividing their given masses by their respective molar masses. The molar mass of aluminum is approximately 26.98 g/mol and of Cl₂ is approximately 70.90 g/mol. Accurate determination of molar mass is imperative for the accurate calculation of moles, which then feeds into working out the stoichiometry of the reaction.

Theoretical Yield

The theoretical yield is the maximum amount of product that can be generated from a given amount of limiting reactant, assuming a 100% efficient reaction with no losses. It's an idealized quantity used to gauge the efficiency of a reaction in a laboratory setting.

For the calculation of the theoretical yield, we first identify the limiting reactant. Then, using the stoichiometry of the reaction, we calculate how many moles of product can be produced, before converting this to grams using the molar mass of the product. In our exercise, the theoretical yield of AlCl₃ based on the limiting reactant Cl₂ was 0.76 grams. It's important to remember that in actual chemical processes, the actual yield is often less than the theoretical yield due to a variety of factors like incomplete reactions, side reactions, or experimental losses.