Problem 100 - Chemistry: The Central Science

Question

Aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) is produced from salicylic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) and acetic anhydride \(\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) : $$ \mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} $$ (a) How much salicylic acid is required to produce \(1.5 \times\) \(10^{2} \mathrm{~kg}\) of aspirin, assuming that all of the salicylic acid is converted to aspirin? (b) How much salicylic acid would be required if only \(80 \%\) of the salicylic acid is converted to aspirin? (c) What is the theoretical yield of aspirin if \(185 \mathrm{~kg}\) of salicylic acid is allowed to react with \(125 \mathrm{~kg}\) of acetic anhydride? (d) If the situation described in part (c) produces \(182 \mathrm{~kg}\) of aspirin, what is the percentage yield?

Step-by-Step Solution

Answer

(a) To produce 150 kg of aspirin with 100% conversion, 115 kg of salicylic acid is required. (b) To produce 150 kg of aspirin with 80% conversion, 144 kg of salicylic acid is required. (c) The theoretical yield of aspirin, given 185 kg of salicylic acid and 125 kg of acetic anhydride, is 221 kg. (d) The percentage yield for the situation described in part (c) is approximately 82.35%.

Step 1: Calculate the molar masses of salicylic acid and aspirin

First, we have to find out the molar masses of salicylic acid (C7H6O3) and aspirin (C9H8O4). Molar mass of salicylic acid = 7 * 12.01 (Carbon) + 6 * 1.01 (Hydrogen) + 3 * 16.00 (Oxygen) = 138.12 g/mol Molar mass of aspirin = 9 * 12.01 (Carbon) + 8 * 1.01 (Hydrogen) + 4 * 16.00 (Oxygen) = 180.16 g/mol

Step 2: Calculate the moles of aspirin produced

Now, let's convert the weight of aspirin produced (150 kg) into moles by using the molar mass. Moles of aspirin = Weight of aspirin / Molar mass of aspirin = (1.5 * 10^5 g) / 180.16 g/mol = 832.50 mol (a) 100% conversion:

Step 3(a): Calculate the required moles of salicylic acid

If 100% of salicylic acid is converted to aspirin, the moles of salicylic acid will be equal to the moles of aspirin produced. Moles of salicylic acid = Moles of aspirin = 832.50 mol

Step 4(a): Calculate the weight of salicylic acid required

Now, let's convert the moles of salicylic acid back to weight: Weight of salicylic acid = Moles of salicylic acid * Molar mass of salicylic acid = 832.50 mol * 138.12 g/mol = 1.15 * 10^5 g = 1.15 * 10^2 kg So, 115 kg of salicylic acid is required for 100% conversion. (b) 80% conversion:

Step 3(b): Calculate the required moles of salicylic acid

If only 80% of salicylic acid is converted, we need to increase the number of moles required by a factor of 1/0.8. Moles of salicylic acid required = Moles of aspirin / 0.8 = 832.50 mol / 0.8 = 1040.62 mol

Step 4(b): Calculate the weight of salicylic acid required

Now, convert the moles of salicylic acid required back to weight: Weight of salicylic acid = Moles of salicylic acid * Molar mass of salicylic acid = 1040.62 mol * 138.12 g/mol = 1.44 * 10^5 g = 1.44 * 10^2 kg So, 144 kg of salicylic acid is required for 80% conversion. (c) Theoretical yield:

Step 5(c): Calculate the moles of reactants

Given the weight of both reactants, first, calculate the moles of each reactant. Moles of salicylic acid = Weight of salicylic acid / Molar mass of salicylic acid = 185 kg * 1000 g/kg / 138.12 g/mol = 1339.97 mol Moles of acetic anhydride = Weight of acetic anhydride / Molar mass of acetic anhydride = 125 kg * 1000 g/kg / 102.09 g/mol = 1224.12 mol

Step 6(c): Determine the limiting reactant

Compare the mole ratio of the reactants to decide which reactant is the limiting one. Since we need 1 mole of salicylic acid for every mole of aspirin produced, and there is less acetic anhydride, the latter will be the limiting reactant.

Step 7(c): Calculate the theoretical yield of aspirin

Now, calculate the theoretical yield of aspirin using the moles of limiting reactant (acetic anhydride): Moles of aspirin = Moles of the limiting reactant = 1224.12 mol Weight of aspirin = Moles of aspirin * Molar mass of aspirin = 1224.12 mol * 180.16 g/mol = 2.21 * 10^5 g = 2.21 * 10^2 kg The theoretical yield of aspirin is 221 kg. (d) Percentage yield:

Step 8(d): Calculate the percentage yield

Given the actual weight (in kg) of aspirin produced (182 kg), calculate the percentage yield: Percentage yield = (Actual yield / Theoretical yield) * 100 = (182 kg / 221 kg) * 100 ≈ 82.35% The answers for each part of the problem are: (a) 115 kg of salicylic acid is required for 100% conversion. (b) 144 kg of salicylic acid is required for 80% conversion. (c) The theoretical yield of aspirin is 221 kg. (d) The percentage yield is 82.35%.

Key Concepts

Molar Mass Calculation

When dealing with chemical reactions, it's essential to know the molar masses of the substances involved. Molar mass represents the mass of one mole of a substance, usually in grams per mole (g/mol). You can calculate it by adding the atomic masses of all atoms present in the compound.

For instance, to find the molar mass of salicylic acid (\(\text{C}_7\text{H}_6\text{O}_3\)), calculate the total of:

• 7 carbon atoms (\(7 \times 12.01\, ext{g/mol}\))
• 6 hydrogen atoms (\(6 \times 1.01\, ext{g/mol}\))
• 3 oxygen atoms (\(3 \times 16.00\, ext{g/mol}\))

Adding these gives a molar mass of 138.12 g/mol for salicylic acid. Similarly, the molar mass of aspirin (\(\text{C}_9\text{H}_8\text{O}_4\)) turns out to be 180.16 g/mol. Calculating molar masses carefully is crucial for accurately converting mass to moles, which is foundational for stoichiometric calculations in reactions.

Limiting Reactant

In any chemical reaction, the limiting reactant is the substance that is completely used up first, thus limiting the amount of product formed. Determining the limiting reactant helps in calculating the theoretical yield, which is the maximum amount of product that can be produced in a reaction.

To identify the limiting reactant, calculate the moles of each reactant present. Compare these quantities against the stoichiometric ratios in the balanced chemical equation. In the reaction provided, 185 kg of salicylic acid and 125 kg of acetic anhydride are used.

Calculate their moles as follows:

• Salicylic acid: \(\frac{185,000\,\text{g}}{138.12\,\text{g/mol}} \approx 1339.97\,\text{mol}\)
• Acetic anhydride: \(\frac{125,000\,\text{g}}{102.09\,\text{g/mol}} \approx 1224.12\,\text{mol}\)

Since each mole of salicylic acid requires one mole of acetic anhydride, and less moles of acetic anhydride are available, it becomes the limiting reactant. This restricts the reaction to the moles of aspirin that can form from the available acetic anhydride.

Percentage Yield

Percentage yield is a measure of how efficient a chemical reaction is. It compares the actual yield obtained from the experiment to the theoretical yield calculated based on stoichiometry. The formula to calculate the percentage yield is:\[\text{Percentage Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right) \times 100\%\]In this exercise, the theoretical yield of aspirin, calculated from the limiting reactant, was 221 kg. However, the actual yield obtained was 182 kg. Plugging these values into the formula:\[\text{Percentage Yield} = \left(\frac{182}{221}\right) \times 100 \approx 82.35\%\]This means about 82.35% of the theoretical yield was achieved in practice. Various factors like impurities, incomplete reactions, or operational losses might cause the percentage yield to be below 100%.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, often represented in a balanced chemical equation. For example, the reaction between salicylic acid and acetic anhydride produces aspirin and acetic acid:\[\text{C}_7\text{H}_6\text{O}_3 + \text{C}_4\text{H}_6\text{O}_3 \rightarrow \text{C}_9\text{H}_8\text{O}_4 + \text{HC}_2\text{H}_3\text{O}_2\] This balanced equation indicates the stoichiometric relationships between reactants and products, meaning:

• 1 mole of salicylic acid reacts with 1 mole of acetic anhydride
• producing 1 mole of aspirin and 1 mole of acetic acid

The stoichiometry of a reaction provides the necessary proportions for calculations involving reactants and products, crucial for determining quantities like the limiting reactant or theoretical yield. Comprehending these relations is vital for successfully conducting and analyzing chemical reactions.