When ethane 1C2H62 reacts with chlorine 1Cl22, the main product is C2H5Cl, but other products containing Cl, such as C2H4Cl2, are also obtained in small quantities. The formation of these other products reduces the yield of C2H5Cl. (a) Calculate the theoretical yield of C2H5Cl when 125 g of C2H6 reacts with 255 g of Cl2, assuming that C2H6 and Cl2 react only to form C2H2Cl and HCl. (b) Calculate the percent yield of C2H5Cl if the reaction produces 206 g of C2H5Cl.

Verified step by step guidance

1. Step 1: Write the balanced chemical equation for the reaction: \[ \text{C}_2\text{H}_6 + \text{Cl}_2 \rightarrow \text{C}_2\text{H}_5\text{Cl} + \text{HCl} \]
2. Step 2: Calculate the molar masses of C2H6 and Cl2. Use the periodic table to find the atomic masses: \[ \text{C}_2\text{H}_6: (2 \times 12.01) + (6 \times 1.01) \text{ g/mol} \] \[ \text{Cl}_2: 2 \times 35.45 \text{ g/mol} \]
3. Step 3: Determine the limiting reactant by calculating the moles of each reactant: \[ \text{Moles of C}_2\text{H}_6 = \frac{125 \text{ g}}{\text{molar mass of C}_2\text{H}_6} \] \[ \text{Moles of Cl}_2 = \frac{255 \text{ g}}{\text{molar mass of Cl}_2} \]
4. Step 4: Use the stoichiometry of the balanced equation to find the theoretical yield of C2H5Cl in moles, based on the limiting reactant. Then convert moles of C2H5Cl to grams using its molar mass: \[ \text{Molar mass of C}_2\text{H}_5\text{Cl} = (2 \times 12.01) + (5 \times 1.01) + 35.45 \text{ g/mol} \]
5. Step 5: Calculate the percent yield using the formula: \[ \text{Percent yield} = \left(\frac{\text{actual yield}}{\text{theoretical yield}}\right) \times 100\% \] where the actual yield is 206 g of C2H5Cl.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It involves using mole ratios derived from the coefficients of the balanced equation to determine how much of each substance is consumed or produced. In this question, stoichiometry is essential for calculating the theoretical yield of C2H5Cl from the given amounts of C2H6 and Cl2.

Theoretical Yield

Theoretical yield is the maximum amount of product that can be generated from a given amount of reactants, assuming complete conversion and no side reactions. It is calculated using stoichiometric relationships from the balanced equation. In this scenario, determining the theoretical yield of C2H5Cl requires knowing the limiting reactant and applying stoichiometry to find the expected mass of the product.

Percent Yield

Percent yield is a measure of the efficiency of a reaction, calculated by dividing the actual yield (the amount of product obtained from the reaction) by the theoretical yield and multiplying by 100. This concept helps assess how well a reaction proceeds under given conditions. In this question, calculating the percent yield of C2H5Cl involves comparing the actual yield of 206 g to the theoretical yield obtained from the stoichiometric calculations.