Question

Chlorine forms from the reaction of hydrochloric acid with manganese(IV) oxide. The balanced equation is: $$\mathrm{MnO}_{2}+4 \mathrm{HCl} \rightarrow \mathrm{MnCl}_{2}+\mathrm{Cl}_{2}+2 \mathrm{H}_{2} \mathrm{O}$$ Calculate the theoretical yield and the percent yield of chlorine if 86.0 \(\mathrm{g}\) of \(\mathrm{MnO}_{2}\) and 50.0 \(\mathrm{g}\) of HCl react. The actual yield of \(\mathrm{Cl}_{2}\) is 20.0 \(\mathrm{g}\)

Short answer

The theoretical yield of Cl2 is 97.03g, and the percent yield is 20.6%.

Step-by-step solution

Identify the limiting reagent

We first find the number of moles of both reactants, MnO2 and HCl. The molar mass of MnO2 is approximately 86.94g/mol and that of HCl is about 36.46g/mol. The number of moles = mass / molar mass. Moles of MnO2 = 86.0g / 86.94g/mol = 0.99 moles. Moles of HCl = 50.0g / 36.46g/mol = 1.37 moles. From the balanced equation, it takes 4 moles of HCl to react with 1 mole of MnO2. So, the necessary amount of HCl for 86g of MnO2 is 0.99 moles * 4 = 3.96 moles, which is more than what we have (1.37 moles), which means HCl is our limiting reagent.

Calculate the theoretical yield

The balanced equation indicates that 1 mole of MnO2 reacts with 4 moles of HCl to produce 1 mole of Cl2, Cl2 has a molar mass of about 70.90g/mol. Therefore, if all the HCl reacted, the theoretical yield of Cl2 would be the number of moles of HCl * molar mass of Cl2 = 1.37 moles * 70.90 g/mol = 97.03g.

Calculate the percent yield

We now have the theoretical yield and the actual yield, so we can compute the percent yield: Percent yield = (actual yield/theoretical yield) * 100 % = (20.0g / 97.03g) * 100 % = 20.6 %. Hence, the theoretical yield of Cl2 is 97.03g and the percent yield is 20.6%.

Key concepts

Limiting Reagent

In chemical reactions, the limiting reagent is the substance that is totally consumed first and thus determines the amount of product that can be formed. Identifying the limiting reagent is important because it helps us calculate the theoretical yield of a reaction.

To determine the limiting reagent, we compare the mole ratio of the reactants used in the reaction with the mole ratio in the balanced chemical equation. If we have fewer moles of one reactant than required by the balanced equation, that reactant is the limiting reagent. In our example, hydrochloric acid (HCl) is identified as the limiting reagent because, according to the balanced equation, we need four times as many moles of HCl than manganese(IV) oxide (MnO2), but in reality, we have a smaller ratio than that.

Stoichiometry

The term stoichiometry comes into play when we deal with the quantitative relationships between reactants and products in a chemical reaction. It involves using the mole ratios from balanced equations to calculate how much of a reactant is needed or how much of a product will be formed.

In our exercise, stoichiometry is applied to predict the mass of chlorine gas that can be produced from given amounts of MnO2 and HCl. We use the mole ratio between MnO2 and Cl2, which according to the balanced equation is 1:1; therefore, we can forecast that 1 mole of MnO2 would lead to 1 mole of Cl2 if the reaction goes to completion.

Chemical Reaction Balancing

Balancing a chemical reaction is crucial for stoichiometry as it ensures the conservation of mass. Each atom that enters a reaction must also be accounted for in the products. To balance a chemical equation, we adjust the coefficients preceding the chemical formulas to get equal numbers of atoms for each element in both reactants and products.

In our scenario, the balanced equation \( \mathrm{MnO}_{2} + 4 \mathrm{HCl} \rightarrow \mathrm{MnCl}_{2} + \mathrm{Cl}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \) shows that one mole of MnO2 reacts with four moles of HCl to produce one mole of Cl2 and two moles of water (H2O), along with MnCl2. The equation is already balanced, reflecting that the number of atoms for each element is equal on both the reactant and product sides.

Mole Concept

The mole concept is a bridge between the atomic world and the macroscopic world. It helps us relate the mass of substances to the number of particles or moles in a sample. One mole is defined as the quantity of a substance that contains the same number of entities (such as atoms, ions, or molecules) as there are atoms in exactly 12 grams of carbon-12.

In practice, we use the molar mass (the mass of one mole of a substance) to convert between grams and moles. For instance, we determined the number of moles of MnO2 by dividing the given mass by its molar mass. This conversion is fundamental to all stoichiometric calculations.