To answer these questions, we need to first understand the concept of theoretical yield and percent yield.
Theoretical yield is the maximum amount of product that can be obtained from a given amount of reactant, assuming complete conversion of reactants to products and no losses. It is calculated using stoichiometry and the balanced chemical equation.
Percent yield is a measure of the efficiency of a chemical reaction. It is the ratio of the actual yield to the theoretical yield, multiplied by 100%.
Let's solve the questions step by step:
1. a. To calculate the theoretical yield, we need to use the stoichiometric ratio between benzene and chlorobenzene from the balanced equation.
According to the balanced equation:
1 mole C6H6 reacts with 1 mole C6H5Cl
We can calculate the molar mass of C6H6 as follows:
C6H6 = 6(12.01 g/mol) + 6(1.01 g/mol) = 78.11 g/mol
Now, we can calculate the moles of C6H6:
moles of C6H6 = mass of C6H6 / molar mass of C6H6
moles of C6H6 = 45.6 g / 78.11 g/mol ≈ 0.584 mol
Since the stoichiometric ratio of C6H6 to C6H5Cl is 1:1, the theoretical yield of C6H5Cl is also 0.584 mol.
To find the mass of C6H5Cl, we need to use its molar mass:
C6H5Cl = 2(12.01 g/mol) + 1(1.01 g/mol) + 1(35.45 g/mol) = 112.56 g/mol
Therefore, the theoretical yield of C6H5Cl is:
theoretical yield = moles of C6H5Cl × molar mass of C6H5Cl
theoretical yield = 0.584 mol × 112.56 g/mol ≈ 65.73 g
b. The percent yield can be calculated using the formula:
percent yield = (actual yield / theoretical yield) × 100%
Given that the actual yield is 63.7 g, and the theoretical yield is 65.73 g (as calculated above), we can substitute these values into the formula to find the percent yield:
percent yield = (63.7 g / 65.73 g) × 100%
percent yield ≈ 96.9%
Therefore, the percent yield of chlorobenzene is approximately 96.9%.
2. a. To calculate the percent yield of sulfur dioxide, we need to use the same formula as before:
percent yield = (actual yield / theoretical yield) × 100%
Given that the actual yield is 40.5 g of SO2, we need to calculate the theoretical yield of SO2.
According to the balanced equation, the stoichiometric ratio of CS2 to SO2 is 1:2. Therefore, the moles of SO2 can be calculated as:
moles of SO2 = moles of CS2 × 2
First, we need to calculate the moles of CS2:
moles of CS2 = mass of CS2 / molar mass of CS2
moles of CS2 = 25.0 g / 76.14 g/mol ≈ 0.328 mol
Now, we can calculate the moles of SO2:
moles of SO2 = 0.328 mol × 2 = 0.656 mol
To find the theoretical yield of SO2, we multiply the moles of SO2 by its molar mass:
theoretical yield = moles of SO2 × molar mass of SO2
theoretical yield = 0.656 mol × (32.07 g/mol) ≈ 21.02 g
Finally, we can substitute the values and calculate the percent yield:
percent yield = (40.5 g / 21.02 g) × 100%
percent yield ≈ 192.5%
Hence, the percent yield of sulfur dioxide is approximately 192.5%.
b. To calculate the percent yield of carbon dioxide, we need to follow the same steps.
Given that 2.5 mol of oxygen react and produce 32.4 g of CO2, we can calculate the theoretical yield of CO2.
According to the balanced equation, the stoichiometric ratio of oxygen to CO2 is 3:1. Therefore, the moles of CO2 can be calculated as:
moles of CO2 = moles of oxygen / 3
First, we need to calculate the moles of oxygen:
moles of oxygen = 2.5 mol
Now, we can calculate the moles of CO2:
moles of CO2 = 2.5 mol / 3 ≈ 0.833 mol
To find the theoretical yield of CO2, we multiply the moles of CO2 by its molar mass:
theoretical yield = moles of CO2 × molar mass of CO2
theoretical yield = 0.833 mol × (44.01 g/mol) ≈ 36.64 g
Finally, we can substitute the values and calculate the percent yield:
percent yield = (32.4 g / 36.64 g) × 100%
percent yield ≈ 88.5%
Therefore, the percent yield of carbon dioxide is approximately 88.5%.