A chemist is commissioned to produce twenty pallets of aspirin: C7H6O3 (salicylic acid) + C4H6O3 (acetic anhydride) → C9H8O4 (aspirin) +C2H4O2 (acetic acid)

Given a bottle contains 500 tablets (each containing 325 mg of aspirin). A case contains 144 bottles. A pallet contains 150 cases.

A 55 gallon drum of acetic anhydride
(density = 1.08 g/mL) costs the chemist $2640.00

A 50 pound bag of salicylic acid costs the chemist $508.00

How many kilograms of salicylic acid are required if the aspirin is produced with a 78.2% yield?

How many liters of acetic anhydride are required?

What is the total cost of the reactants used?

To calculate the amount of salicylic acid required, we need to determine the number of moles of aspirin produced. Since the balanced equation tells us that 1 mole of salicylic acid produces 1 mole of aspirin, and the yield is given as 78.2%, we can use the following steps:

1. Calculate the mass of aspirin per tablet:
Each tablet contains 325 mg of aspirin, which is equal to 0.325 g.

2. Calculate the number of moles of aspirin produced per tablet:
Using the molar mass of aspirin (C9H8O4), which is 180.16 g/mol, we can calculate the number of moles per tablet:
0.325 g / 180.16 g/mol = 0.0018 mol.

3. Calculate the number of moles of salicylic acid required:
Since the yield is given as 78.2%, we divide the number of moles of aspirin by the yield percentage:
0.0018 mol / 0.782 = 0.0023 mol.

4. Calculate the mass of salicylic acid required:
Multiply the number of moles of salicylic acid by its molar mass (C7H6O3 = 138.12 g/mol):
0.0023 mol * 138.12 g/mol = 0.317 g.

Now, let's calculate the number of liters of acetic anhydride required:

1. Determine the volume of acetic anhydride in gallons:
The drum contains 55 gallons.

2. Convert gallons to liters:
1 gallon = 3.78541 liters, so 55 gallons is equal to 55 * 3.78541 = 207.20455 liters.

Finally, let's calculate the total cost of the reactants:

1. Calculate the cost of salicylic acid per kilogram:
The cost of a 50-pound bag of salicylic acid is $508.00. To convert pounds to kilograms, divide by 2.2046:
50 pounds / 2.2046 = 22.68 kg.
Therefore, the cost per kilogram of salicylic acid is $508.00 / 22.68 kg = $22.38/kg.

2. Calculate the cost of salicylic acid:
Multiply the mass of salicylic acid required (0.317 g) by the cost per kilogram ($22.38/kg):
0.317 kg * $22.38/kg = $7.10.

3. Calculate the cost of acetic anhydride:
The cost of a 55-gallon drum is $2640.00.

Hence, the total cost of the reactants used is $7.10 + $2640.00 = $2647.10.

To find the number of kilograms of salicylic acid required, we need to consider the molecular weights of the compounds involved in the reaction.

1. Calculate the molecular weight of salicylic acid (C7H6O3):
C (12.01 g/mol) x 7 + H (1.01 g/mol) x 6 + O (16.00 g/mol) x 3 = 138.12 g/mol

2. Since a mole of salicylic acid weighs 138.12 g, we can calculate the number of moles needed using the desired mass of aspirin:
Mass of aspirin = 20 pallets x 150 cases x 144 bottles x 500 tablets x 325 mg = 8,280,000 mg
Moles of aspirin = (8,280,000 mg / 1000) / (325 mg/mol) = 25,473.85 mol

3. The actual yield is given as 78.2%, so we can calculate the required mass of salicylic acid:
Mass of salicylic acid required = (25,473.85 mol / 0.782) x 138.12 g/mol = 9,070,646.06 g

4. Convert grams to kilograms:
Mass of salicylic acid required = 9,070,646.06 g / 1000 = 9070.65 kg

Therefore, 9070.65 kilograms of salicylic acid are required for the production of twenty pallets of aspirin.

To find the number of liters of acetic anhydride required, we can use the density and molecular weight.

1. Calculate the molecular weight of acetic anhydride (C4H6O3):
C (12.01 g/mol) x 4 + H (1.01 g/mol) x 6 + O (16.00 g/mol) x 3 = 102.09 g/mol

2. Calculate the density of acetic anhydride:
Density = 1.08 g/mL

3. Calculate the volume of acetic anhydride required:
Mass of acetic anhydride = 55 gallons x 3.78541 L/gallon x 1,000 g/L = 207,378.55 g
Volume of acetic anhydride = Mass of acetic anhydride / Density = 207,378.55 g / 1.08 g/mL ≈ 192,063.77 mL

4. Convert milliliters to liters:
Volume of acetic anhydride = 192,063.77 mL / 1000 = 192.06 L

Therefore, approximately 192.06 liters of acetic anhydride are required.

To calculate the total cost of the reactants used, we need to multiply the quantities used by their respective costs.

1. Cost of the salicylic acid:
Cost of the salicylic acid required = 9070.65 kg x $508.00/kg = $4,605,942.20

2. Cost of the acetic anhydride (in liters):
Cost of the acetic anhydride required = 192.06 L x $2640.00/L = $506,894.40

3. Total cost of the reactants:
Total cost = Cost of the salicylic acid + Cost of the acetic anhydride required
Total cost = $4,605,942.20 + $506,894.40 = $5,112,836.60

Therefore, the total cost of the reactants used is approximately $5,112,836.60.