Question

DDT, an insecticide harmful to fish, birds, and humans, is produced by the following reaction: $$2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}+\mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{9} \mathrm{Cl}_{5}+\mathrm{H}_{2} \mathrm{O}$$ In a government lab, 1142 g of chlorobenzene is reacted with 485 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 \(1038.16~g\). b. The limiting reactant is chloral (\(C_2HOCl_3\)), and the reactant in excess is chlorobenzene (\(C_6H_5Cl\)). c. The mass of the excess reactant leftover is \(482.69~g\) of chlorobenzene. d. The percent yield of DDT in the reaction is \(19.28\%\).

Step-by-step solution

Calculating moles of reactants

First, we need to find the number of moles of each reactant using the respective molar mass. \(C_6H_5Cl\) has a molar mass of \((6 \cdot 12.01)+(5 \cdot 1.01)+(1 \cdot 35.45)=112.56~g/mol\). \(C_2HOCl_3\) has a molar mass of \((2 \cdot 12.01)+(1 \cdot 1.01)+(3 \cdot 35.45)=165.37~g/mol\). So for chlorobenzene, moles = \(\frac{1142}{112.56} = 10.15 ~mol\) For chloral, moles = \(\frac{485}{165.37} = 2.93 ~mol\)

Identifying the limiting reactant

To identify the limiting reactant, we first need to find the mole ratio of the reactants according to the balanced chemical equation: \(2~C_6H_5Cl + C_2HOCl_3 \rightarrow C_{14}H_9Cl_5 + H_2O\) The mole ratio of \(C_6H_5Cl\) to \(C_2HOCl_3\) is 2:1. Now, let's find the mole ratio using the given moles of reactants: \(\frac{10.15~mol}{2} = 5.075\) Since the mole ratio of the given reactants (5.075) is greater than the required mole ratio (2:1), this means that chloral (C2HOCl3) is the limiting reactant, while chlorobenzene (C6H5Cl) is in excess.

Calculating the mass of DDT formed

Given that the reaction has 100% yield, we can calculate the amount of DDT formed based on the limiting reactant. The molar mass of DDT is \((14 \cdot 12.01) + (9 \cdot 1.01) + (5 \cdot 35.45) = 354.49~g/mol\). According to the balanced chemical equation, 1 mole of chloral produces 1 mole of DDT. So, mass of DDT = moles of DDT x molar mass of DDT = \(2.93 ~mol \cdot 354.49 ~g/mol = 1038.16 ~g\)

Calculating the mass of leftover reactant

To calculate the mass of the excess reactant leftover after the reaction, we first need to find how much of the chlorobenzene actually reacted using the mole ratio: Required moles of chlorobenzene = 2 x moles of limiting reactant = 2 x 2.93 = 5.86 mol. Then, let's calculate the leftover moles of chlorobenzene and their mass: Leftover moles of chlorobenzene = Initial moles - Required moles = 10.15 - 5.86 = 4.29 mol So, the mass of leftover chlorobenzene = \(4.29 ~mol \cdot 112.56 ~g/mol = 482.69 ~g\)

Calculating the percent yield

Now that we have actual yield and theoretical yield, we can calculate the percentage yield as follows: Percent Yield = \(\frac{Actual~Yield}{Theoretical~Yield} \cdot 100\) Percent Yield = \(\frac{200.0}{1038.16} \cdot 100 = 19.28 \%.\) To summarize the answers to each part of the exercise: a. The mass of DDT formed, assuming 100% yield, is 1038.16 g. b. The limiting reactant is chloral (C2HOCl3), and the reactant in excess is chlorobenzene (C6H5Cl). c. The mass of the excess reactant leftover is 482.69 g of chlorobenzene. d. The percent yield of DDT in the reaction is 19.28%.

Key concepts

Limiting Reactant

Understanding the limiting reactant is crucial when working through stoichiometry problems. It's akin to a bottleneck in a production line—this is the reactant that runs out first, thus limiting the amount of product that can be formed in a chemical reaction. To determine the limiting reactant, calculate the number of moles of each reactant given their masses and molar masses. Then, use the balanced chemical equation to find the stoichiometric ratios and identify which reactant is used up first, given the actual amounts present.

To enhance this concept, remember that the limiting reactant dictates the theoretical maximum amount of product—once it's exhausted, the reaction can't proceed further, regardless of how much of the other reactants remains.

Theoretical Yield

The theoretical yield is the maximum amount of product that can be generated from a given amount of limiting reactant, assuming perfect conditions where no material is lost and the reaction goes to completion. Calculating the theoretical yield requires the mole-to-mole conversion between reactants and products, as dictated by the balanced chemical equation. Imagine it as the best-case scenario outcome.

Incorporating this into a real-world context, imagine you're baking cookies and you have the exact ingredients for 24 cookies—the theoretical yield is 24 cookies, assuming you followed the recipe perfectly and no dough was left sticking to the bowl or your fingers.

Percent Yield

The concept of percent yield comes into play when comparing the efficiency of a laboratory reaction versus the ideal scenario. It's calculated by dividing the actual yield (the amount of product actually obtained from the experiment) by the theoretical yield and then multiplying by 100 to get a percentage. The percent yield can tell us a lot about a reaction, like how practical it might be on a larger scale or if there were any errors or unexpected side reactions during the process.

For example, if you only obtained 18 cookies from the expected 24, your percent yield would be \(\frac{18}{24} \cdot 100 = 75\%\), reflecting the efficiency of your cookie-making process.

Molar Mass

The molar mass of a substance is the mass of one mole of its particles (atoms, molecules, ions, etc.) and is represented in grams per mole (g/mol). It is determined by summing the atomic masses of all atoms present in a molecule, as found on the periodic table. Molar mass serves as a conversion factor between the mass of a substance and the number of moles, and is fundamental to all stoichiometry calculations.

If you're working with a complex compound, like the insecticide DDT in our exercise, calculating its molar mass accurately is key for determining the stoichiometry of the reaction and thus, everything from the limiting reactant to the theoretical and percent yields.