Problem 97 - Chemistry Matter and Change

Question

Chlorine forms from the reaction of hydrochloric acid with manganese(IV) oxide. The balanced equation is: \begin{equation} \mathrm{MnO}_{2}+4 \mathrm{HCl} \rightarrow \mathrm{MnCl}_{2}+\mathrm{Cl}_{2}+2 \mathrm{H}_{2} \mathrm{O} \end{equation} 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 \(\mathrm{HCl}\) react. The actual yield of \(\mathrm{Cl}_{2}\) is 20.0 \(\mathrm{g}\) .

Step-by-Step Solution

Answer

The theoretical yield of \(\mathrm{Cl}_2\) is approximately 24.33 g, and the percent yield is 82.20%.

Step 1: Determine molar masses

Find the molar mass of each compound involved in the reaction. The molar masses are: \(\mathrm{MnO}_2 = 86.94\, \text{g/mol} \), \(\mathrm{HCl} = 36.46\, \text{g/mol} \), \(\mathrm{Cl}_2 = 70.90\, \text{g/mol} \).

Step 2: Calculate moles of reactants

Convert the given masses to moles. For \(\mathrm{MnO}_2\), \[\text{moles of } \mathrm{MnO}_2 = \frac{86.0\, \text{g}}{86.94\, \text{g/mol}} \approx 0.989\, \text{moles}\]. For \(\mathrm{HCl}\), \[\text{moles of } \mathrm{HCl} = \frac{50.0\, \text{g}}{36.46\, \text{g/mol}} \approx 1.372\, \text{moles}\].

Step 3: Identify the limiting reactant

The stoichiometric ratio from the balanced equation is \(1:4\) for \(\mathrm{MnO}_2\) to \(\mathrm{HCl}\). Compare the available moles: \(0.989\) moles \(\mathrm{MnO}_2\) requires \(0.989 \times 4 = 3.956\) moles of \(\mathrm{HCl}\), more than available \((1.372)\). Thus, \(\mathrm{HCl}\) is the limiting reactant.

Step 4: Calculate theoretical yield of \(\mathrm{Cl}_2\)

Using the stoichiometry, \(4\) moles of \(\mathrm{HCl}\) produce \(1\) mole of \(\mathrm{Cl}_2\). Theoretical moles of \(\mathrm{Cl}_2\) = \(1.372 / 4 = 0.343\) moles. Theoretical yield in grams: \[\text{mass of theoretical yield} = 0.343 \times 70.90\, \text{g/mol} \approx 24.33\, \text{g}\].

Step 5: Calculate percent yield

Compare the actual yield to the theoretical yield. \[\text{Percent yield} = \left(\frac{20.0\, \text{g}}{24.33\, \text{g}}\right) \times 100\% \approx 82.20\%\].

Key Concepts

Theoretical Yield

Theoretical yield is a key concept in stoichiometry that refers to the maximum amount of product that can be formed in a chemical reaction, based on the quantities of the reactants used, according to the stoichiometric ratios in the balanced chemical equation. It assumes all reactants convert into the desired product without any loss.

To calculate the theoretical yield, you need to follow these steps:

• First, identify the balanced equation for the chemical reaction. This provides the mole ratio between the reactants and products.
• Next, determine the number of moles of reactants you have, by using their masses and molar masses.
• Use stoichiometry to find the number of moles of the product expected. Finally, multiply the moles of product by its molar mass to find the theoretical yield in grams.

Understanding this concept is crucial, as it helps predict how efficient a reaction could be under ideal conditions.

Limiting Reactant

In every chemical reaction, one of the reactants will be consumed before the others, stopping the reaction from proceeding. This reactant is called the limiting reactant. It determines the maximum amount of product that can be produced in the reaction.

Finding the limiting reactant requires comparing the mole ratio of the reactants used in the experiment to the mole ratio in the balanced equation.

• Calculate the moles of each reactant available.
• Use the balanced equation to find out how much each reactant needs based on the other reactants.
• The reactant that runs out first, according to these calculations, is your limiting reactant.

Knowing the limiting reactant helps in calculating the theoretical yield accurately and is essential for optimizing reactions for maximum product yield.

Percent Yield

Percent yield provides a means of comparing the efficiency of a chemical reaction by using the ratio of the actual yield (the amount of product you actually obtain from the reaction) to the theoretical yield.

To calculate percent yield, you simply use the formula: \[ \text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\% \] This gives you a percentage that tells you how effective your reaction was in converting the reactants into the desired product. A higher percent yield indicates a more efficient reaction. Actual and theoretical yields can differ due to a variety of factors, such as side reactions, incomplete reactions, or practical losses during the experimental process. Understanding percent yield is vital for assessing and improving reaction conditions.