In the commercial production of the element arsenic, arsenic (II) oxide is heated with carbon which reduces the oxide to the metal according to the following equation: 2As2O3 + 3C ----„³ 3CO2 +4As
A>if 8.87 g of As2O3 is used in the reaction and 5.33 g of As is produced what is the percentage yield?
B>If 67 of carbon is used up in a different reaction and 425 g of As is produced, calculate the percentage yield of this reaction
Worked another place.
To calculate the percentage yield in both scenarios, you need to use the formula:
Percentage Yield = (Actual Yield / Theoretical Yield) x 100%
Let's calculate the theoretical yield in each case first.
A) Calculation for scenario A:
Given:
- Mass of As2O3 used = 8.87 g
- Mass of As produced = 5.33 g
According to the balanced equation, the molar ratio between As2O3 and As is 2:4. Therefore, we need to find the molar masses of As2O3 and As to convert the masses into moles.
Molar mass of As2O3 = 2(74.92 g/mol) + 3(16.00 g/mol) = 197.84 g/mol
Molar mass of As = 74.92 g/mol
Next, we can use the molar masses to find the number of moles of As2O3 and As.
Moles of As2O3 = 8.87 g / 197.84 g/mol ≈ 0.045 moles
Moles of As = 5.33 g / 74.92 g/mol ≈ 0.071 moles
According to the balanced equation, the molar ratio between As2O3 and As is 2:4. So, the theoretical yield (in moles) of As is twice the moles of As2O3 used.
Theoretical yield of As = 2 x 0.045 moles = 0.09 moles
Now we need to convert the theoretical yield back into grams.
Theoretical yield of As = 0.09 moles x 74.92 g/mol ≈ 6.74 g
B) Calculation for scenario B:
Given:
- Mass of carbon used = 67 g
- Mass of As produced = 425 g
First, let's determine the moles of carbon used in the reaction.
Molar mass of carbon (C) = 12.01 g/mol
Moles of carbon (C) = 67 g / 12.01 g/mol ≈ 5.58 moles
According to the balanced equation, the molar ratio between carbon (C) and As is 3:4, so the number of moles of As produced would be:
Moles of As produced = 5.58 moles x (4/3) ≈ 7.44 moles
Finally, we can calculate the theoretical yield of As by converting the moles to grams:
Theoretical yield of As = 7.44 moles x 74.92 g/mol ≈ 557.44 g
Now that we have the theoretical yield for both scenarios, we can proceed to calculate the percentage yield.
A) For scenario A:
Percentage Yield = (Actual Yield / Theoretical Yield) x 100%
= (5.33 g / 6.74 g) x 100%
≈ 79.1%
B) For scenario B:
Percentage Yield = (Actual Yield / Theoretical Yield) x 100%
= (425 g / 557.44 g) x 100%
≈ 76.3%
Therefore, in scenario A, the percentage yield is approximately 79.1%, and in scenario B, the percentage yield is approximately 76.3%.