Aspirin (C9H8O4) is produced from salicylic acid (C7H6O3), and acetic anhydride (C4H6O3):

C7H6O3 + C4H6O3 �¨ C9H8O4 + HC2H3O2 .

(c) What is the theoretical yield of aspirin if 189 kg of salicylic acid is allowed to react with 128 kg of acetic anhydride?

(d) If the situation described in part (c) produces 117 kg of aspirin, what is the percentage yield?

(c) Well, to find the theoretical yield, we need to first calculate the limiting reactant. Let's do some math, but don't worry, I won't make it too painful.

First, we need to convert the masses of salicylic acid and acetic anhydride to moles. For salicylic acid, we'll use its molar mass of approximately 138.1 g/mol: 189 kg = 189,000 g, so we have 189,000 g / 138.1 g/mol = approximately 1,369.8 mol.

For acetic anhydride, with a molar mass of roughly 102.1 g/mol: 128 kg = 128,000 g, which gives us 128,000 g / 102.1 g/mol = approximately 1,254.6 mol.

Now, let's compare the mole ratios of salicylic acid and acetic anhydride in the balanced equation. From the equation, we see that one mole of salicylic acid reacts with one mole of acetic anhydride to produce one mole of aspirin.

Since mole ratios are equal, it means that salicylic acid and acetic anhydride have the same stoichiometry in this reaction. Therefore, the limiting reactant is the one that is present in a smaller quantity, which in this case is salicylic acid with 1,369.8 mol.

The theoretical yield of aspirin can now be calculated using the molar mass of aspirin, which is approximately 180.2 g/mol: 1,369.8 mol * 180.2 g/mol = approximately 246,965.96 g or 246.97 kg.

So, the theoretical yield of aspirin is around 246.97 kg.

(d) Now, let's calculate the percentage yield. To do that, we divide the actual yield (117 kg) by the theoretical yield (246.97 kg) and multiply by 100:

(117 kg / 246.97 kg) * 100 = approximately 47.37%

So, the percentage yield is about 47.37%. It seems like the reaction didn't produce as much aspirin as we expected. Maybe some molecules got cold feet and skipped the party!

To find the theoretical yield of aspirin, we need to calculate the number of moles of salicylic acid and acetic anhydride and determine which reactant is limiting.

First, we find the molar masses of the compounds:
- Molar mass of salicylic acid (C7H6O3): 138.12 g/mol
- Molar mass of acetic anhydride (C4H6O3): 102.09 g/mol
- Molar mass of aspirin (C9H8O4): 180.16 g/mol

(c) Calculating the theoretical yield of aspirin:
1. Convert the masses of salicylic acid and acetic anhydride to moles:
- Moles of salicylic acid = 189 kg / (138.12 g/mol) = 1367.72 mol
- Moles of acetic anhydride = 128 kg / (102.09 g/mol) = 1253.28 mol

2. Determine the limiting reactant by comparing the moles of each reactant:
The ratio of moles of salicylic acid to acetic anhydride is approximately 1:1.
Since the moles of salicylic acid are greater, it is not in excess, and therefore it is the limiting reactant.

3. Determine the theoretical yield of aspirin using the stoichiometry of the balanced equation:
From the balanced equation, the ratio of salicylic acid to aspirin is 1:1.
Thus, the moles of aspirin produced will be equal to the moles of salicylic acid used = 1367.72 mol.

Calculate the mass of aspirin:
Mass of aspirin = Moles of aspirin * Molar mass of aspirin
Mass of aspirin = 1367.72 mol * 180.16 g/mol = 246.40 kg

Therefore, the theoretical yield of aspirin is 246.40 kg.

(d) To calculate the percentage yield, we divide the actual yield by the theoretical yield and multiply by 100:

Percentage yield = (Actual yield / Theoretical yield) * 100
Percentage yield = (117 kg / 246.40 kg) * 100
Percentage yield ≈ 47.5%

Therefore, the percentage yield of aspirin is approximately 47.5%.

To find the theoretical yield of aspirin, we need to calculate the amount of aspirin that can be produced based on the balanced chemical equation. The balanced equation states that 1 mole of salicylic acid reacts with 1 mole of acetic anhydride to produce 1 mole of aspirin and 1 mole of acetic acid.

Step 1: Convert the given masses of salicylic acid and acetic anhydride to moles.
To do this, we divide the given masses by their respective molar masses:

Molar mass of salicylic acid (C7H6O3):
C: 12.01 g/mol * 7 = 84.07 g/mol
H: 1.01 g/mol * 6 = 6.06 g/mol
O: 16.00 g/mol * 3 = 48.00 g/mol
Total molar mass = 84.07 g/mol + 6.06 g/mol + 48.00 g/mol = 138.13 g/mol

Moles of salicylic acid = 189 kg / 138.13 g/mol = 1,368.6 moles

Molar mass of acetic anhydride (C4H6O3):
C: 12.01 g/mol * 4 = 48.04 g/mol
H: 1.01 g/mol * 6 = 6.06 g/mol
O: 16.00 g/mol * 3 = 48.00 g/mol
Total molar mass = 48.04 g/mol + 6.06 g/mol + 48.00 g/mol = 102.10 g/mol

Moles of acetic anhydride = 128 kg / 102.10 g/mol = 1,254.5 moles

Step 2: Determine the limiting reactant.
The limiting reactant is the reactant that is completely consumed and determines the maximum amount of product that can be formed. To find the limiting reactant, we compare the moles of salicylic acid and acetic anhydride.

From the balanced equation, we can see that the ratio of salicylic acid to aspirin is 1:1. This means that 1 mole of salicylic acid can produce 1 mole of aspirin.

Similarly, we can see that the ratio of acetic anhydride to aspirin is also 1:1.

Since the moles of salicylic acid and acetic anhydride are equal (1,368.6 moles vs. 1,254.5 moles), neither is in excess. Therefore, the limiting reactant is either salicylic acid or acetic anhydride.

Step 3: Calculate the theoretical yield.
Since both reactants are in a 1:1 ratio with the product, we can choose either the moles of salicylic acid or acetic anhydride to determine the amount of aspirin that can be formed.

Theoretical yield of aspirin = moles of salicylic acid (or acetic anhydride) = 1,368.6 moles

Step 4: Convert the moles of aspirin to mass.
To convert moles of aspirin to mass, we multiply the moles by the molar mass of aspirin (C9H8O4).

Molar mass of aspirin (C9H8O4):
C: 12.01 g/mol * 9 = 108.09 g/mol
H: 1.01 g/mol * 8 = 8.08 g/mol
O: 16.00 g/mol * 4 = 64.00 g/mol
Total molar mass = 108.09 g/mol + 8.08 g/mol + 64.00 g/mol = 180.17 g/mol

Theoretical yield of aspirin = 1,368.6 moles * 180.17 g/mol = 246,765.6 g = 246.8 kg (rounded to three significant figures).

Therefore, the theoretical yield of aspirin is 246.8 kg.

To find the percentage yield, we compare the actual yield to the theoretical yield.

Actual yield of aspirin = 117 kg

Percentage yield = (Actual yield / Theoretical yield) * 100
Percentage yield = (117 kg / 246.8 kg) * 100
Percentage yield = 47.4% (rounded to one decimal place)

Therefore, the percentage yield is 47.4%.