To calculate the percentage yield of a reaction, we need to compare the actual yield to the theoretical yield and then calculate the percentage.
A) First, let's calculate the theoretical yield of As in this reaction. We are given that 8.87 g of As2O3 is used.
The molar mass of As2O3 is 197.84 g/mol, so we can calculate the number of moles of As2O3 used:
Moles of As2O3 = Mass of As2O3 / Molar mass of As2O3
Moles of As2O3 = 8.87 g / 197.84 g/mol
Moles of As2O3 = 0.0448 mol
From the balanced chemical equation, we can see that the stoichiometric ratio between As2O3 and As is 2:4 or 1:2.
Therefore, the number of moles of As produced is twice the number of moles of As2O3 used:
Moles of As = 2 * Moles of As2O3
Moles of As = 2 * 0.0448 mol
Moles of As = 0.0896 mol
Now, we can calculate the theoretical yield of As:
Theoretical yield of As = Moles of As * Molar mass of As
Theoretical yield of As = 0.0896 mol * 74.92 g/mol
Theoretical yield of As = 6.71 g
The percentage yield is then calculated by dividing the actual yield by the theoretical yield and multiplying by 100:
Percentage yield = (Actual yield / Theoretical yield) * 100
Percentage yield = (5.33 g / 6.71 g) * 100
Percentage yield = 79.5%
B) In this case, we are given that 67 g of carbon is used up and 425 g of As is produced. We need to calculate the percentage yield.
First, we need to find the number of moles of carbon used:
Moles of C = Mass of C / Molar mass of C
Moles of C = 67 g / 12.01 g/mol
Moles of C = 5.58 mol
From the balanced chemical equation, we can see that the stoichiometric ratio between C and As is 3:4. Therefore, the number of moles of As produced is:
Moles of As = (4/3) * Moles of C
Moles of As = (4/3) * 5.58 mol
Moles of As = 7.45 mol
Now, let's calculate the theoretical yield of As:
Theoretical yield of As = Moles of As * Molar mass of As
Theoretical yield of As = 7.45 mol * 74.92 g/mol
Theoretical yield of As = 557 g
The percentage yield is then calculated by dividing the actual yield by the theoretical yield and multiplying by 100:
Percentage yield = (Actual yield / Theoretical yield) * 100
Percentage yield = (425 g / 557 g) * 100
Percentage yield = 76.3%