Problem 72 - Chemistry The Molecular Science

Question

Aspirin is produced by the reaction of salicylic acid and acetic anhydride. $$\begin{array}{cc}2 \mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}(\mathrm{~s})+\mathrm{C}_{4} \mathrm{H}_{6}\mathrm{O}_{3}(\ell) \longrightarrow 2 \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{O}(\ell) \\\\\begin{array}{c} \text { salicylic } \\\\\text { acid }\end{array} & \begin{array}{c} \text { acetic } \\\\\text { anhydride }\end{array} & \text { aspirin }\end{array}$$ If you mix \(100 . \mathrm{g}\) of each of the reactants, calculate the maximum mass of aspirin that can be obtained.

Step-by-Step Solution

Answer

130.4 g of aspirin.

Step 1: Write the Balanced Chemical Equation

The balanced chemical equation given is: \[ 2 \ \text{C}_{7}\text{H}_6\text{O}_3 (s) + \text{C}_{4}\text{H}_6\text{O}_3 (\ell) \rightarrow 2 \ \text{C}_{9}\text{H}_8\text{O}_4 (s) + \text{H}_2\text{O} (\ell) \] This tells us that 2 moles of salicylic acid reacts with 1 mole of acetic anhydride to produce 2 moles of aspirin and 1 mole of water.

Step 2: Calculate Molar Masses

Using the periodic table, calculate the molar masses: \[ \text{Salicylic acid (C}_7\text{H}_6\text{O}_3): (7\times12.01) + (6\times1.008) + (3\times16.00) = 138.12 \, \text{g/mol} \] \[ \text{Acetic anhydride (C}_4\text{H}_6\text{O}_3): (4\times12.01) + (6\times1.008) + (3\times16.00) = 102.09 \, \text{g/mol} \] \[ \text{Aspirin (C}_9\text{H}_8\text{O}_4): (9\times12.01) + (8\times1.008) + (4\times16.00) = 180.16 \, \text{g/mol} \]

Step 3: Determine Moles of Reactants

Convert the masses of the reactants to moles: \[ \text{Moles of salicylic acid} = \frac{100 \, \text{g}}{138.12 \, \text{g/mol}} \approx 0.724 \, \text{mol} \] \[ \text{Moles of acetic anhydride} = \frac{100 \, \text{g}}{102.09 \, \text{g/mol}} \approx 0.980 \, \text{mol} \]

Step 4: Identify the Limiting Reactant

According to the reaction, 2 moles of salicylic acid react with 1 mole of acetic anhydride. We have 0.724 moles of salicylic acid available. Therefore, we need \(0.362\) moles of acetic anhydride (since \(0.724/2 = 0.362\)). Since we have \(0.980\) moles of acetic anhydride, salicylic acid is the limiting reactant.

Step 5: Calculate Maximum Mass of Aspirin

Since salicylic acid is the limiting reactant and we have 0.724 moles of it, this will produce an equivalent of 0.724 moles of aspirin. The mass of aspirin formed can be calculated by: \[ \text{Mass of aspirin} = 0.724 \, \text{mol} \times 180.16 \, \text{g/mol} \approx 130.4 \, \text{g} \]

Key Concepts

Chemical Reaction Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction.
In the reactions, the coefficients in the balanced equation indicate the number of moles of each substance involved.
This guides the calculations to determine how much product can be formed from given quantities of reactants.
For aspirin synthesis, the balanced chemical equation tells us that:

• 2 moles of salicylic acid react with 1 mole of acetic anhydride.
• The same number of moles (2) of aspirin are produced along with water.

Understanding stoichiometry is essential as it enables chemists to make predictions about chemical reactions.

Limiting Reactant

The limiting reactant is the substance that is entirely used up in a chemical reaction and determines the amount of product formed.
Identifying the limiting reactant is crucial because it directly affects the yield of the reaction.
In this aspirin synthesis, we evaluate the moles of reactants.
Salicylic acid is the limiting reactant, because:

• 2 moles of salicylic acid are required for every mole of acetic anhydride used.
• The reaction cannot produce more aspirin than what the available salicylic acid can react to make.

Knowing the limiting reactant allows you to accurately calculate the maximum possible amount of product.

Molar Mass Calculation

Calculating molar mass is an important step in chemical reactions, as it allows for the conversion between grams and moles.
By using the atomic masses from the periodic table, you can determine the molar masses of substances involved:

• Salicylic acid (C\(_7\)H\(_6\)O\(_3\)) is calculated by adding the weighted average of the masses of 7 carbon, 6 hydrogen, and 3 oxygen atoms.
• Acetic anhydride (C\(_4\)H\(_6\)O\(_3\)) follows a similar process, considering 4 carbon, 6 hydrogen, and 3 oxygen atoms.
• Aspirin (C\(_9\)H\(_8\)O\(_4\)) requires calculations for 9 carbon, 8 hydrogen, and 4 oxygen atoms.

Accurate molar mass calculations are critical in determining moles from a given mass of a compound, facilitating stoichiometric calculations.

Balanced Chemical Equation

A balanced chemical equation provides essential information about the reactant and product amounts relative to one another.
It maintains the law of conservation of mass, where the number of atoms of each element is equal on both sides of the equation.
For aspirin production, the equation is: \[ 2 \ ext{C}_{7}\text{H}_6\text{O}_3 (s) + \ ext{C}_{4}\text{H}_6\text{O}_3 (\ell) \rightarrow 2 \ ext{C}_{9}\text{H}_8\text{O}_4 (s) + \ ext{H}_2\text{O} (\ell) \] This shows how 2 moles of salicylic acid react with 1 mole of acetic anhydride to produce 2 moles of aspirin and 1 mole of water.
Balancing equations ensures the chemical reaction is represented accurately for calculations like determining the limiting reactant and potential yield of products.