Chapter 12, Problem 55A

Interpretation Introduction

Interpretation: To identify the limiting reagent in the given reaction.

Concept Introduction: The formation of products is dependent on the number of reactants. The reactant that is consumed first is known as the limiting reactant; when this reactant is consumed completely, then there will be no more formation of products.

Answer to Problem 55A

The limiting reagent is phosphoric acid.

Explanation of Solution

The given chemical reaction is depicted as follows:

  ${\text{H}}_3{\text{PO}}_4\left(aq\right)+3\text{NaOH}\left(aq\right)\to {\text{Na}}_{\text{3}}{\text{PO}}_{\text{4}}\left(aq\right)+3{\text{ H}}_2\text{O}\left(l\right)$

When one mole of phosphoric acid reacts with three moles of sodium hydroxide it yields one mole of sodium phosphate and three moles of water.

Calculation for moles of sodium hydroxide is as follows:

  $1.75\cancel{{\text{mol H}}_3{\text{PO}}_4}\times \frac{3\text{mol NaOH}}{1\cancel{{\text{mol H}}_3{\text{PO}}_4}}=5.25\text{ mol NaOH}$

Calculation for moles of phosphoric acid is as follows:

  $5.0\cancel{\text{mol NaOH}}\times \frac{{\text{1 mol H}}_3{\text{PO}}_4}{3\cancel{\text{mol NaOH}}}=1.67{\text{ mol H}}_3{\text{PO}}_4$

Thus, the reactant that is consumed first is phosphoric acid as the number of moles is less than sodium.

Conclusion

Thus, the limiting reagent is phosphoric acid.