Problem 110 - Chemistry An Atoms First Approach

Question

Aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) is synthesized by reacting salicylic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) with acetic anhydride \(\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right) .\) The balanced equation is $$\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}$$ a. What mass of acetic anhydride is needed to completely consume \(1.00 \times 10^{2}\) g salicylic acid? b. What is the maximum mass of aspirin (the theoretical yield) that could be produced in this reaction?

Step-by-Step Solution

Answer

a. The mass of acetic anhydride needed to completely consume 100 g of salicylic acid is 73.91 g. b. The maximum mass of aspirin (theoretical yield) that could be produced in this reaction is 130.44 g.

Step 1: Calculate the moles of salicylic acid given

Using the molar mass of salicylic acid (C7H6O3), we can find the moles of salicylic acid in the given mass: Molar mass of salicylic acid = \(7 \times 12.01\) (for C) \(+ 6 \times 1.01\) (for H) \(+ 3 \times 16.00\) (for O) = 138.12 g/mol Given mass of salicylic acid = 100 g Moles of salicylic acid = \(\frac{\text{Given mass}}{\text{Molar mass}}\) Moles of salicylic acid = \(\frac{100\,\text{g}}{138.12\,\text{g/mol}}\) = 0.724 moles

Step 2: Calculate the moles of acetic anhydride required

From the balanced equation, 1 mole of salicylic acid reacts with 1 mole of acetic anhydride. Therefore, we can find the moles of acetic anhydride required: Moles of acetic anhydride = moles of salicylic acid = 0.724 moles

Step 3: Calculate the mass of acetic anhydride required

Using the molar mass of acetic anhydride (C4H6O3), we can find the mass of acetic anhydride required: Molar mass of acetic anhydride = \(4 \times 12.01\) (for C) \(+ 6 \times 1.01\) (for H) \(+ 3 \times 16.00\) (for O) = 102.09 g/mol Mass of acetic anhydride = moles of acetic anhydride × molar mass of acetic anhydride Mass of acetic anhydride = \(0.724\, \text{moles} \times 102.09\, \text{g/mol}\) = 73.91 g a. The mass of acetic anhydride needed to completely consume 100 g of salicylic acid is 73.91 g.

Step 4: Calculate the moles of aspirin produced

From the balanced equation, 1 mole of salicylic acid produces 1 mole of aspirin. Therefore, we can find the moles of aspirin produced: Moles of aspirin = moles of salicylic acid = 0.724 moles

Step 5: Calculate the maximum mass of aspirin produced

Using the molar mass of aspirin (C9H8O4), we can find the maximum mass of aspirin produced: Molar mass of aspirin = \(9 \times 12.01\) (for C) \(+ 8 \times 1.01\) (for H) \(+ 4 \times 16.00\) (for O) = 180.16 g/mol Mass of aspirin = moles of aspirin × molar mass of aspirin Mass of aspirin = \(0.724\, \text{moles} \times 180.16\, \text{g/mol}\) = 130.44 g b. The maximum mass of aspirin (theoretical yield) that could be produced in this reaction is 130.44 g.

Key Concepts

Chemical Reactions

A chemical reaction occurs when substances combine to form new substances. In our example, salicylic acid (C\(_7\)H\(_6\)O\(_3\)) reacts with acetic anhydride (C\(_4\)H\(_6\)O\(_3\)) to produce aspirin (C\(_9\)H\(_8\)O\(_4\)) and acetic acid (HC\(_2\)H\(_3\)O\(_2\)).
Chemical equations are used to represent these reactions. They show the substances involved in the reaction as well as the ratio in which they react and are produced.
In this reaction, the balanced equation shows a 1:1 ratio for both reactants and products:

• Salicylic Acid: 1 mole
• Acetic Anhydride: 1 mole
• Aspirin: 1 mole
• Acetic Acid: 1 mole

This 1:1 molar ratio allows us to predict the amount of product formed when a known amount of reactants are used.

Molar Mass Calculation

Molar mass is a key concept when working with chemicals, as it helps us convert between grams and moles. The molar mass of a compound is the sum of the atomic masses of all atoms in a molecule.
To find the molar mass:

• Identify the number of each type of atom in the compound.
• Multiply the atomic mass of each atom by the number of atoms present.
• Sum these values to get the total molar mass.

For instance, the molar mass of salicylic acid (C\(_7\)H\(_6\)O\(_3\)) was calculated as follows:

• Carbon (C): 7 atoms × 12.01 g/mol = 84.07 g/mol
• Hydrogen (H): 6 atoms × 1.01 g/mol = 6.06 g/mol
• Oxygen (O): 3 atoms × 16.00 g/mol = 48.00 g/mol

Adding these gives a molar mass of 138.12 g/mol for salicylic acid. Similar steps are carried out for finding the molar masses of acetic anhydride and aspirin.
This calculation is crucial because it helps determine the number of moles when we have a given mass of a substance.

Theoretical Yield

Theoretical yield is the maximum amount of product that can be obtained in a chemical reaction. It's based on the stoichiometry of the balanced chemical equation.
In our reaction, for every mole of salicylic acid, we ideally get one mole of aspirin. This means that knowing the amount of salicylic acid we start with allows us to calculate the maximum aspirin output.
To find the theoretical yield:

• Determine the number of moles of the limiting reactant (the reactant that will be completely used up first).
• Use the stoichiometry from the balanced equation to find the moles of desired product, in this case, aspirin.
• Convert the moles of this product to mass using its molar mass.

For instance, if we start with 100 g of salicylic acid (0.724 moles), we calculate the mass of aspirin by multiplying the moles of aspirin produced by its molar mass (180.16 g/mol). This gives a theoretical yield of 130.44 g aspirin.
Understanding theoretical yield helps compare it to actual yield obtained experimentally, to determine efficiency of the reaction.