Problem 78 - Chemistry: The Central Science

Question

When ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) reacts with chlorine \(\left(\mathrm{Cl}_{2}\right)\), the main product is \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl} ;\) but other products containing \(\mathrm{Cl}\), such as \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\), are also obtained in small quantities. The formation of these other products reduces the yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\). (a) Calculate the theoretical yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) when \(125 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{6}\) reacts with \(255 \mathrm{~g}\) of \(\mathrm{Cl}_{2}\), assuming that \(\mathrm{C}_{2} \mathrm{H}_{6}\) and \(\mathrm{Cl}_{2}\) react only to form \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) and \(\mathrm{HCl}\). (b) Calculate the percent yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) if the reaction produces \(206 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\).

Step-by-Step Solution

Answer

The theoretical yield of C2H5Cl is 232.27 g and the percent yield of C2H5Cl in the reaction is 88.69%.

Step 1: Balanced Chemical Equation

Write the balanced chemical equation for the reaction: \[ C_{2}H_{6} + Cl_{2} \rightarrow C_{2}H_{5}Cl + HCl \]

Step 2: Calculate the Moles of reactants

Calculate the moles of C2H6 and Cl2 by dividing the mass by their molar masses. The molar mass of C2H6 is (12.01*2) + (1.01*6) = 30.07 g/mol and Cl2 is (35.45*2) = 70.90 g/mol. Moles of C2H6 = \( \frac{125 g}{30.07 g/mol} \) = 4.16mol Moles of Cl2 = \( \frac{255 g}{70.90 g/mol} \) = 3.60mol

Step 3: Identify the Limiting Reactant

Compare the molar ratios of the reactants with their stoichiometric coefficients to find the limiting reactant. From the balanced equation, the molar ratio of C2H6 to Cl2 is 1:1. C2H6: \( \frac{4.16 mol}{1} \) = 4.16 Cl2: \( \frac{3.60 mol}{1} \) = 3.60 Since the value for Cl2 is smaller, Cl2 is the limiting reactant.

Step 4: Calculate the Theoretical Yield of C2H5Cl

Use stoichiometry to calculate the theoretical yield of C2H5Cl, based on the limiting reactant, Cl2. The molar mass of C2H5Cl is (12.01*2) + (1.01*5) + 35.45 = 64.52 g/mol. Moles of C2H5Cl = Moles of Cl2 (Limiting reactant) = 3.60 mol Theoretical Yield of C2H5Cl = \( 3.60 mol \times 64.52 g/mol \) = 232.27 g

Step 5: Calculate the Percent Yield

To calculate the percent yield, divide the actual yield (206 g) by the theoretical yield (232.27 g) and multiply by 100. Percent Yield = \( \frac{206 g}{232.27 g} \times 100\) = 88.69% The percent yield of C2H5Cl in the reaction is 88.69%.

Key Concepts

Theoretical Yield

When preparing to calculate the amount of product formed in a chemical reaction, the theoretical yield is the maximum quantity of product that can be generated as predicted by stoichiometry, assuming complete consumption of the limiting reactant. It's determined by using the balanced chemical equation and considering the molar ratios of reactants and products.

The theoretical yield serves as a benchmark to measure the efficiency of the reaction. While it assumes a perfect scenario without any losses or side reactions, in reality, many factors such as incomplete reactions or competing reactions can lead to a lower actual yield.

Limiting Reactant

In chemical reactions, the limiting reactant is the substance that is completely consumed first, restricting the amount of product formed. It's essential to identify the limiting reactant because it determines the theoretical yield of the reaction. This is an important concept in stoichiometry, where one begins with the quantities of reactants in order to predict the output of product(s).

To find out which reactant it is, calculate and compare the number of moles of each reactant that would be required to completely react according to the balanced chemical equation. The reactant that is present in the lesser quantity, based on the molar ratios, is the limiting reactant.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction, based on the conservation of mass and the coefficients from the balanced chemical equation. It involves calculations that predict the amounts of substances consumed and produced. By using stoichiometry, you can determine the amounts of reactants you need to obtain a desired quantity of product or the amount of product you can get from the reactants available.

Stoichiometry requires a balanced chemical equation, a grasp of molar masses, and an understanding of mole-to-mole conversions. The fundamental principle behind stoichiometry is the mole ratio, which is derived from the coefficients of the balanced equation, and it's pivotal in all quantitative analyses of chemical reactions.

Chemical Reaction

A chemical reaction is a process that transforms one or more substances into different substances. The substances that undergo change are called reactants, and the new substances formed are called products. Chemical reactions are characterized by the breaking and forming of chemical bonds and involve the rearrangement of atoms.

Every reaction can be depicted by a balanced chemical equation that visually represents the transformation of reactants into products, where the atoms' conservation is maintained. It's crucial to understand this concept to grasp the changes occurring at the molecular level that lead to observable changes during a chemical reaction.

Balanced Chemical Equation

A balanced chemical equation provides a symbolic representation of a chemical reaction where both sides of the equation contain the same number of atoms of each element. The balancing of an equation adheres to the law of conservation of mass, and it's essential for performing accurate stoichiometric calculations.

To balance an equation, coefficients are placed in front of the chemical formulas to ensure that the number of atoms of each element is the same on both the reactants and products side. A properly balanced chemical equation is critical for determining stoichiometric ratios, which are used to calculate theoretical yields and to identify the limiting reactant in a reaction.