To determine the limiting reactant in this scenario, we need to follow a step-by-step approach that involves using the masses of the reactants, their molar masses, and the stoichiometric coefficients from the balanced chemical equation. Let's break down the problem:
1. Calculate the number of moles of each reactant:
The molar masses of the reactants are given:
- Molar mass of salicylic acid [tex]\(( C _7 H _6 O _3 )\)[/tex] is 138.12 g/mol.
- Molar mass of acetic anhydride [tex]\(( C _4 H _6 O _3 )\)[/tex] is 102.09 g/mol.
Given masses:
- Mass of salicylic acid = 70.0 g.
- Mass of acetic anhydride = 80.0 g.
[tex]\[
\text{Moles of salicylic acid} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{70.0 \, \text{g}}{138.12 \, \text{g/mol}} \approx 0.5068 \, \text{mol}
\][/tex]
[tex]\[
\text{Moles of acetic anhydride} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{80.0 \, \text{g}}{102.09 \, \text{g/mol}} \approx 0.7836 \, \text{mol}
\][/tex]
2. Determine the stoichiometric ratios:
According to the balanced chemical equation:
[tex]\[
2 \text{ moles of } C _7 H _6 O _3 \text{ react with 1 mole of } C _4 H _6 O _3
\][/tex]
To determine the limiting reactant, we compare the actual mole ratios of the reactants to the stoichiometric ratios.
[tex]\[
\text{Stoichiometric ratio of salicylic acid} = \frac{\text{Moles of salicylic acid}}{\text{Stoichiometric coefficient of salicylic acid}} = \frac{0.5068}{2} \approx 0.2534
\][/tex]
[tex]\[
\text{Stoichiometric ratio of acetic anhydride} = \frac{\text{Moles of acetic anhydride}}{\text{Stoichiometric coefficient of acetic anhydride}} = \frac{0.7836}{1} \approx 0.7836
\][/tex]
3. Identify the limiting reactant:
The limiting reactant is the one with the smallest stoichiometric ratio, as it will be completely consumed first during the reaction, thereby limiting the extent of the reaction.
Comparing the stoichiometric ratios:
- Salicylic acid: 0.2534
- Acetic anhydride: 0.7836
Since the stoichiometric ratio for salicylic acid (0.2534) is less than that for acetic anhydride (0.7836), salicylic acid is the limiting reactant.
Thus, the limiting reactant is salicylic acid.
