Question

DDT, an insecticide harmful to fish, birds, and humans, is produced by the following reaction: $$ 2 \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl}+\mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{9} \mathrm{Cl}_{5}+\mathrm{H}_{2} \mathrm{O} $$ \(\begin{array}{lll}\text { chlorobenzene } & \text { chloral } & \text { DDT }\end{array}\) In a government lab, \(1142 \mathrm{~g}\) of chlorobenzene is reacted with \(485 \mathrm{~g}\) of chloral. a. What mass of DDT is formed, assuming \(100 \%\) yield? b. Which reactant is limiting? Which is in excess? c. What mass of the excess reactant is left over? d. If the actual yield of DDT is \(200.0 \mathrm{~g}\), what is the percent yield?

Short answer

a. The mass of DDT formed assuming 100% yield is \(1042.23 \, g\). b. Chloral is the limiting reactant, and chlorobenzene is in excess. c. The mass of the excess reactant (chlorobenzene) left over is \(481.35 \, g\). d. The percent yield of DDT is \(19.2\%\).

Step-by-step solution

Calculate the number of moles of reactants

First, we need to find the molar masses of chlorobenzene and chloral. Chlorobenzene: \(C_6H_3Cl = (6 \times 12.01) + (3 \times 1.01) + (1 \times 35.45) = 112.39 \, g/mol\) Chloral: \(C_2HOCl_3 = (2 \times 12.01) + (1 \times 1.01) + (1 \times 16.00) + (3 \times 35.45) = 164.92 \, g/mol\) Next, we can find the number of moles of both reactants. Chlorobenzene: \(\frac{1142 \, g}{112.39 \, g/mol} = 10.16 \, mol\) Chloral: \(\frac{485 \, g}{164.92 \, g/mol} = 2.94 \, mol\)

Determine the limiting reactant and excess reactant

The reaction stoichiometry is 2 moles of chlorobenzene reacting with 1 mole of chloral. We can determine the limiting reactant by dividing the moles of each reactant with their coefficients. Chlorobenzene: \(\frac{10.16 \, mol}{2} = 5.08\) Chloral: \(\frac{2.94 \, mol}{1} = 2.94\) Since the value of chloral (2.94) is lower than chlorobenzene (5.08), it means chloral is the limiting reactant, while chlorobenzene is in excess.

Calculate the mass of DDT produced assuming 100% yield

Knowing the limiting reactant, we can now calculate the mass of DDT produced assuming 100% yield. The molar mass of DDT is: \(C_{14}H_9Cl_5 = (14 \times 12.01) + (9 \times 1.01) + (5 \times 35.45) = 354.50 \, g/mol\) From the balanced reaction, it is seen that 1 mole of chloral produces 1 mole of DDT: \[2.94 \, mol \, ( \text{chloral}) \times \frac{1 \, mol \,( \text{DDT})}{1 \, mol \, ( \text{chloral})} = 2.94 \, mol \, ( \text{DDT})\] We can now find the mass of DDT produced: \(2.94 \, mol \, (\text{DDT}) \times 354.50 \, g/mol = 1042.23 \, g\) Thus, the mass of DDT formed is 1042.23 g assuming 100% yield.

Find the mass of the excess reactant left over

Since chlorobenzene is in excess, we need to find the amount of chlorobenzene consumed and then subtract it from the initial mass. Moles of chlorobenzene consumed: \(2.94 \, mol \, (\text{chloral}) \times \frac{2 \, mol \,( \text{chlorobenzene})}{1 \, mol \, ( \text{chloral})} = 5.88 \, mol\) Mass of chlorobenzene consumed: \(5.88 \, mol \times 112.39 \, g/mol = 660.65 \, g\) Mass of chlorobenzene left over: \(1142 \, g - 660.65 \, g = 481.35 \, g\) Therefore, 481.35 g of excess reactant (chlorobenzene) is left over.

Calculate the percent yield of DDT

Given that the actual yield of DDT is 200 g, we can now compute the percent yield. Percent yield: \(\frac{\text{Actual yield}}{\text{Theoretical yield}} \times 100\%\) Percent yield: \(\frac{200 \, g}{1042.23 \, g} \times 100\% = 19.2\%\) Hence, the percent yield of the reaction is 19.2%.

Key concepts

Limiting Reactant

In chemical reactions, reactants combine in precise ratios to form products. However, when quantities of reactants are not in exact stoichiometric proportions—meaning the ratios defined by the balanced chemical equation—then one reactant will be completely consumed before the others. This is known as the limiting reactant. To identify the limiting reactant, we compare the mole ratios of the reactants to the coefficients in the balanced equation. In our example, chloral is the limiting reactant because it will be used up first, thus determining the maximum amount of DDT that can be formed. Understanding which reactant is limiting is crucial because it establishes the possible yield of the product and indicates if there will be any reactants left over.

Percent Yield

The efficiency or success of a chemical reaction in producing the desired product can be measured through the percent yield. It is calculated by dividing the actual yield—what you actually get from the reaction—by the theoretical yield—the amount predicted by stoichiometry assuming everything goes perfectly—and then multiplying by 100%. The percent yield can indicate the presence of side reactions, loss of material, measurement inaccuracies, or incomplete reactions. For instance, the calculated 19.2% yield in our problem is quite low, suggesting practical hurdles in the reaction process or in the post-reaction handling that significantly reduced the final quantity of DDT.

Theoretical Yield

The concept of theoretical yield is pivotal in stoichiometry. It's the maximum amount of product that can be generated from a given amount of reactants, assuming no loss of material and that the reaction goes to completion. We calculate it using the balanced chemical equation and the limiting reactant's amount. The assumptions of 100% efficiency in this calculation help in benchmarking the actual yield and in planning the quantities of reactants needed. However, in reality, achieving the theoretical yield is rare due to various practical limitations.

Molar Mass

A fundamental concept in chemistry is molar mass, the weight of one mole of a substance—usually expressed in grams per mole (g/mol). This number is vital as it serves as a conversion factor between mass and moles of a substance, linking the molecular scale to the practical scale. The molar masses of reactants and products are pertinent in determining the stoichiometry of chemical reactions. For example, calculating the molar masses of chlorobenzene and chloral enables us to determine the moles of each that participated in the reaction. Always ensure that the molar masses used in calculations are accurate and that atomic weights are taken from the periodic table.

Reaction Stoichiometry

Understanding reaction stoichiometry involves the quantitative analysis of the balanced chemical equation. It allows chemists to predict the amounts of reactants needed and products formed in a chemical reaction. Reaction stoichiometry uses the molar ratios of the substances involved to relate their quantities. For example, in our exercise, it was necessary to understand that two moles of chlorobenzene react with one mole of chloral to form DDT. This stoichiometric relationship serves as the backbone for all subsequent calculations, including the amount of product formed and the excess reactant(s) remaining after the reaction.