Question

DDT, an insecticide harmful to fish, birds, and humans, is produced by the following reaction: $$ 2 \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl}+\mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{4} \mathrm{Cl}_{5}+\mathrm{H}_{2} \mathrm{O} $$ \(\begin{array}{ll}\text { orobenzenc chloral } & \mathrm{D}\end{array}\) In a government lab, \(1142 \mathrm{~g}\) of chlorobenzene is reacted with \(485 \mathrm{~g}\) of chloral. a. What mass of DDT is formed? 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 is 1165 g. b. Chloral (C2HOCl3) is the limiting reactant, and chlorobenzene (C6H3Cl) is the excess reactant. c. The mass of the excess reactant left over is 401.63 g. d. The percent yield is 17.17%.

Step-by-step solution

Write down and balance the chemical equation

Our given balanced chemical equation is: $$ 2 \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl}(\text{chlorobenzene})+\mathrm{C}_{2} \mathrm{HOCl}_{3}(\text{chloral}) \longrightarrow \mathrm{C}_{14} \mathrm{H}_{4} \mathrm{Cl}_{5}(\text{DDT})+\mathrm{H}_{2} \mathrm{O} $$

Convert mass of reactants to moles

To do this, we will divide the given mass by the molar mass of each reactant. Molar mass of chlorobenzene (C6H3Cl) = 112.5 g/mol Moles of chlorobenzene = 1142 g / 112.5 g/mol = 10.15 mol Molar mass of chloral (C2HOCl3) = 147.5 g/mol Moles of chloral = 485 g / 147.5 = 3.29 mol

Determine the limiting reactant

To determine the limiting reactant, we will use stoichiometry relating the moles of reactants. The given balanced equation: $$ 2 \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl} + \mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{4} \mathrm{Cl}_{5}+\mathrm{H}_{2}\mathrm{O} $$ We use mole ratios to see which reactant runs out first: 10.15 mol C6H3Cl / 2 (it's stoichiometric coefficient) = 5.075 3.29 mol C2HOCl3 / 1 = 3.29 Since 3.29 < 5.075, chloral (C2HOCl3) is the limiting reactant.

Calculate the mass of DDT produced

Using stoichiometry with the limiting reactant, we can calculate the mass of DDT produced. Molar mass of DDT (C14H4Cl5) = 354.5 g/mol Moles of DDT = moles of chloral * (1 mol DDT / 1 mol chloral) = 3.29 mol Mass of DDT = moles of DDT * molar mass of DDT = 3.29 * 354.5 = 1165 g

Determine mass of excess reactant left over

Now, we will find the mass of the excess reactant (chlorobenzene) left over. We start by calculating the amount of chlorobenzene that reacted with chloral: Moles of chlorobenzene that reacted = moles of chloral * (2 mol C6H3Cl / 1 mol C2HOCl3) = 3.29 * 2 = 6.58 mol Now subtract the moles of chlorobenzene that reacted from the initial moles of chlorobenzene: Moles of chlorobenzene left = 10.15 - 6.58 = 3.57 mol Mass of chlorobenzene left = moles of chlorobenzene left * molar mass of C6H3Cl = 3.57 * 112.5 = 401.63 g

Calculate the percent yield

Given that the actual yield of DDT is 200.0 g, we can calculate the percent yield. Percent yield = (actual yield / theoretical yield) * 100 = (200 / 1165) * 100 = 17.17% In summary: a. The mass of DDT formed is 1165 g. b. The limiting reactant is chloral (C2HOCl3) and the excess reactant is chlorobenzene (C6H3Cl). c. The mass of the excess reactant left over is 401.63 g. d. The percent yield is 17.17%.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that helps us quantify the amounts of reactants and products in a chemical reaction. By using balanced chemical equations, stoichiometry allows us to determine the proportions in which different substances react and form new compounds. In the exercise above, we start with a balanced chemical equation: \[ 2 \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl} + \mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{4} \mathrm{Cl}_{5} + \mathrm{H}_{2} \mathrm{O} \]
This reaction shows that two moles of chlorobenzene react with one mole of chloral to produce one mole of DDT and one mole of water. The coefficients in the equation represent the molar ratio of the substances.

To solve problems using stoichiometry, follow these steps:

• Write and balance the chemical equation, ensuring the number of atoms for each element is the same on both sides.
• Convert the mass of each reactant to moles using their molar masses.
• Use mole ratios derived from the balanced equation to determine which reactant is the limiting one, which dictates how much product can be formed.
• Calculate how much product is produced using the moles of the limiting reactant.

This step-by-step method is crucial for solving many chemistry problems, ensuring that calculations are accurate and logical.

Percent Yield

Percent yield is a measure in chemistry that tells us how efficient a chemical reaction is in producing the desired product. It compares the actual amount of product obtained from a reaction to the theoretical amount predicted by stoichiometry. The formula to calculate percent yield is:
\[ \text{Percent Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right) \times 100 \]
In practice, reactions rarely go to completion without any loss, side reactions, or errors in measurement, so the actual yield is often less than the theoretical one.

In the DDT production example, the theoretical yield was calculated as \(1165 \text{ g}\). However, the actual yield was only \(200.0 \text{ g}\), resulting in a percent yield of \(17.17\%\).
This low percent yield indicates significant loss or inefficiency in the reaction process.

Some factors that can affect percent yield include:

• Incomplete reactions where not all reactants fully convert to products.
• Side reactions that produce undesired by-products.
• Loss of product during processing, such as during filtering or transferring substances.
• Purity of reactants, where impurities can reduce the effective amount of material reacting.

Understanding percent yield is essential for scientists and engineers who work to optimize reactions for industrial and research applications.

Chemical Reactions

Chemical reactions are processes in which substances called reactants are transformed into different substances known as products. These transformations involve breaking chemical bonds in the reactants and forming new ones in the products, following the rules of chemical equations.

In the case of DDT's production, we start with chlorobenzene and chloral as reactants. When they react, chemical bonds are reorganized to form DDT and water. The equation provided is balanced, meaning it accurately represents the conservation of atoms for each element involved in the reaction:
\[ 2 \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl} + \mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{4} \mathrm{Cl}_{5} + \mathrm{H}_{2} \mathrm{O} \]
Chemical reactions can be described by different types, such as synthesis, decomposition, single replacement, and double replacement reactions, each with unique characteristics. Here, the reaction synthesis, as it combines smaller molecules into a larger one, forming DDT from chlorobenzene and chloral.

Understanding chemical reactions involves recognizing:

• Reactants and products, including their chemical formulas and structures.
• Balancing chemical equations to maintain the conservation of mass.
• Energy changes that occur, often determining whether reactions absorb or release energy (endothermic vs. exothermic).

By learning these aspects, we gain insight into the mechanisms that drive chemical changes, forming the foundation of chemistry as a science.