Question

Aluminum sulfate can be made by the following reaction. \(2 \mathrm{AlCl}_{3}(a q)+3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+6 \mathrm{HCl}(a q)\) It is quite soluble in water, so to isolate it the solution has to be evaporated to dryness. This drives off the volatile \(\mathrm{HCl},\) but the residual solid has to be heated to a little over \(200^{\circ} \mathrm{C}\) to drive off all of the water. In one experiment, \(25.0 \mathrm{~g}\) of \(\mathrm{AlCl}_{3}\) was mixed with \(30.0 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). Eventually, \(28.46 \mathrm{~g}\) of pure \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) was isolated. Calculate the percentage yield.

Short answer

The actual yield of Al2(SO4)3 is 28.46 g. After calculating moles and determining the limiting reactant, the theoretical yield is calculated. Then, percentage yield is calculated using the ratio of actual yield to theoretical yield, multiplied by 100%.

Step-by-step solution

- Calculate the moles of reactants

Determine the number of moles of both aluminum chloride (AlCl3) and sulfuric acid (H2SO4) using their respective molar masses. The molar mass of AlCl3 is approximately 133.34 g/mol, and for H2SO4 it is approximately 98.08 g/mol.For AlCl3: Number of moles = mass in grams / molar mass = 25.0 g / 133.34 g/mol.For H2SO4: Number of moles = mass in grams / molar mass = 30.0 g / 98.08 g/mol.

- Determine the limiting reactant

The balanced reaction shows a 2:3 molar ratio between AlCl3 and H2SO4. Calculate the actual molar ratio from the moles obtained in Step 1 and compare to the theoretical ratio to determine which reactant will be exhausted first, thus limiting the amount of product that can be formed.

- Calculate the theoretical yield

Using the moles of the limiting reactant, calculate the amount of Al2(SO4)3 that could theoretically be produced, based on the stoichiometry of the balanced equation. The stoichiometry shows that 2 moles of AlCl3 produce 1 mole of Al2(SO4)3.

- Calculate the percentage yield

The percentage yield is determined by the actual yield (the mass of product actually obtained) divided by the theoretical yield (the mass that should have been obtained if the reaction went to completion), multiplied by 100%.Percentage yield = (actual yield / theoretical yield) x 100%.

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that involves calculating the quantities of reactants and products in chemical reactions. Fundamentally, it's based on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Therefore, the amount of each element must be the same in the reactants and products.

Using the balanced chemical equation, stoichiometry allows the prediction of how much product will be formed from given quantities of reactants or vice versa. It requires a balanced equation because this shows the exact proportions in which chemicals combine and react. When performing stoichiometric calculations, we often use the molar mass of substances to convert between grams and moles, allowing us to use the molar ratios from the balanced equation effectively.

In the given exercise, stoichiometry is used to determine the amount of aluminum sulfate produced from aluminum chloride and sulfuric acid. By knowing the balanced equation and the molar mass of the reactants, we can calculate the moles of each reactant and, subsequently, the theoretical yield of the product.

Limiting Reactant

The limiting reactant in a chemical reaction is the substance that is wholly consumed first, thus determining the maximum amount of product that can be formed. It is 'limiting' because its quantity limits the progress of the reaction; once it is used up, the reaction stops, even if other reactants are still present in excess.

To identify the limiting reactant, we compare the molar amounts of all reactants to their stoichiometric ratios in the balanced equation. The reactant that provides the lesser amount of product, based on these ratios, is the limiting reactant. In the exercise, by calculating and comparing the moles of aluminum chloride and sulfuric acid, it can be deduced which one will run out first during the reaction, thus inhibiting further production of the aluminum sulfate product.

Understanding which reactant is limiting is crucial for calculating the theoretical yield — a key step before determining the percentage yield.

Molar Mass

The molar mass is the weight of one mole of a substance, usually expressed in grams per mole (g/mol). This physical property is essential for converting between the mass of a substance and the amount in moles, facilitating stoichiometric calculations in chemical reactions.

Every element on the periodic table has an atomic weight, which closely approximates the molar mass of that element. For compounds, the molar mass is the sum of the atomic weights of all atoms in the molecule. For instance, in the provided exercise, the molar mass of aluminum chloride (AlCl3) and sulfuric acid (H2SO4) are used to determine how many moles of each reactant are present, which is the first step in finding the limiting reactant and subsequently, the theoretical yield.

Theoretical Yield

The theoretical yield is the amount of product that would be generated if a chemical reaction proceeded perfectly and to completion, with no losses. It's a calculated value, using stoichiometry and assuming that the limiting reactant reacts entirely to form products.

To calculate the theoretical yield, one must first determine the limiting reactant and then use the stoichiometric relationship from the balanced equation to find out how much product could be made from the amount of limiting reactant available. In the example exercise, after identifying the limiting reactant, the stoichiometry of the balanced chemical equation is used to predict the maximum amount of aluminum sulfate that could be produced if all goes according to plan. The theoretical yield is a vital step in determining the efficiency of the reaction through the percentage yield.

Chemical Reactions

Chemical reactions involve the transformation of one or more substances (reactants) into different substances (products). Every chemical reaction is governed by a balanced chemical equation that tells us the proportions in which reactants combine to form products.

Chemical reactions can be classified into various types such as synthesis, decomposition, single replacement, double replacement, and combustion. Understanding the type of reaction helps in setting up equations and predicting the products. The reaction in the exercise is a double replacement reaction, where parts of two compounds are exchanged to form two new compounds. The equation also shows the states of the reactants and products, indicating that aluminum sulfate is in an aqueous solution initially and then isolated by evaporating the water and volatilizing the by-product hydrochloric acid. Knowledge of the type of reaction and the state of products is key to understanding the steps involved in isolating and purifying the final product.