Problem 18 - Chemistry and Chemical Reactivity

Question

Aspirin, \(\mathrm{C}_{6} \mathrm{H}_{4}\left(\mathrm{OCOCH}_{3}\right) \mathrm{CO}_{2} \mathrm{H},\) is produced by the reaction of salicylic acid, \(\mathrm{C}_{6} \mathrm{H}_{4}(\mathrm{OH}) \mathrm{CO}_{2} \mathrm{H}\) and acetic anhydride, \(\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O}\) (page 182 ). $$\mathrm{C}_{6} \mathrm{H}_{4}(\mathrm{OH}) \mathrm{CO}_{2} \mathrm{H}(\mathrm{s})+\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O}(\ell) \rightarrow \mathrm{C}_{6} \mathrm{H}_{4}\left(\mathrm{OCOCH}_{3}\right) \mathrm{CO}_{2} \mathrm{H}(\mathrm{s})+\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\ell)$$ If you mix \(100 .\) g of each of the reactants, what is the maximum mass of aspirin that can be obtained?

Step-by-Step Solution

Answer

The maximum mass of aspirin that can be obtained is approximately 130.44 g.

Step 1: Identify Limiting Reactant

First, we determine which reactant is the limiting reactant by calculating the moles of each reactant. The molar mass of salicylic acid, \( \mathrm{C}_{6} \mathrm{H}_{4}(\mathrm{OH}) \mathrm{CO}_{2} \mathrm{H} \), is approximately 138.12 g/mol. For acetic anhydride, \( (\mathrm{CH}_{3}\mathrm{CO})_{2} \mathrm{O} \), the molar mass is about 102.09 g/mol. We calculate the moles of each: - Moles of salicylic acid = \( \frac{100\, \text{g}}{138.12\, \text{g/mol}} \approx 0.724\, \text{mol} \) - Moles of acetic anhydride = \( \frac{100\, \text{g}}{102.09\, \text{g/mol}} \approx 0.980\, \text{mol} \)Since the reaction consumes 1 mole of each reactant per mole of aspirin produced, salicylic acid is the limiting reactant.

Step 2: Calculate Theoretical Yield of Aspirin

Using the moles of the limiting reactant (salicylic acid), we calculate the maximum moles of aspirin that can be produced. Since 1 mole of salicylic acid produces 1 mole of aspirin, the maximum moles of aspirin is 0.724 mol. Next, we calculate the mass of aspirin. The molar mass of aspirin, \( \mathrm{C}_{6} \mathrm{H}_{4}(\mathrm{OCOCH}_{3}) \mathrm{CO}_{2} \mathrm{H} \), is approximately 180.16 g/mol.- Mass of aspirin = \( 0.724 \times 180.16\, \text{g/mol} \approx 130.44\, \text{g} \).

Key Concepts

Theoretical Yield

The idea of theoretical yield is like trying to calculate the maximum amount of product you can get from a chemical reaction, assuming everything goes perfectly without any loss. When you're working with chemical reactions, sometimes not all of the reactants are used up, which means the actual yield may be less than what was expected.
To find the theoretical yield, you first need to identify the limiting reactant. This is the reactant that will run out first and stop the reaction from producing more product. In our reaction between salicylic acid and acetic anhydride to make aspirin, salicylic acid was the limiting reactant.

• Figure out which reactant is limiting by comparing the molar amounts.
• Use the limiting reactant to determine the maximum moles of product that can be formed.
• Convert these moles into grams using the product's molar mass.

So, once you know how many moles of aspirin can theoretically be made from the limiting reactant, you simply multiply that by aspirin's molar mass (180.16 g/mol) to get the maximum mass of aspirin possible.

Molar Mass Calculation

Molar mass is essentially the weight of one mole of a chemical compound and is crucial in stoichiometry calculations. It's the sum of the atomic masses of all atoms in a molecule as listed on the periodic table.
To calculate the molar mass:

• Identify each element in a compound and its number of atoms.
• Multiply the atomic mass of each element by the number of times it appears in the compound.
• Add all those values together for the total molar mass.

For instance, the molar mass of salicylic acid \(\mathrm{C}_{6} \mathrm{H}_{4}(\mathrm{OH}) \mathrm{CO}_{2} \mathrm{H}\) was about 138.12 g/mol. If you dissect it:

• Carbon \(12.01\, \text{g/mol} * 7\)
• Hydrogen \(1.01\, \text{g/mol} * 6\)
• Oxygen \(16.00\, \text{g/mol} * 3\)

Adding these gives you the molar mass needed for further calculations like finding out how many moles are in a given gram.

Chemical Equation Balancing

Balancing chemical equations is the process of making sure you have the same number of each type of atom on both sides of the reaction. It's a fundamental concept in chemistry, crucial for accurately predicting the products and their amounts.
To balance a chemical equation:

• Write down the unbalanced equation.
• Count the number of atoms of each element on both sides of the equation.
• Add coefficients to balance the atoms for each element one at a time. Start with the most complex molecule.
• Check your work to ensure both sides are balanced.

In the reaction of salicylic acid and acetic anhydride to form aspirin, ensuring our equation was balanced helped us confidently proceed with other calculations. The balanced equation also affirms that one mole of salicylic acid reacts with one mole of acetic anhydride, assuring that our stoichiometry calculation is correct.