91Ó°ÊÓ

In chemical reactions, the limiting reactant is the reactant that runs out first. This happens because it is consumed completely while the other reactants may still be left in excess. The quantity of the limiting reactant determines the amount of products that can be formed.

To identify the limiting reactant, we need to use the balanced chemical equation and the initial amount of each reactant. In this exercise, we deal with magnesium hydroxide, \( \mathrm{Mg(OH)}_2 \), and nitric acid, \( \mathrm{HNO}_3 \). The balanced chemical equation is:

• \( \mathrm{Mg(OH)}_2 + 2\mathrm{HNO}_3 \rightarrow \mathrm{Mg(NO}_3)_2 + 2\mathrm{H}_2\mathrm{O} \)

For every 1 mole of \( \mathrm{Mg(OH)}_2 \), 2 moles of \( \mathrm{HNO}_3 \) are required. By calculating the moles of both reactants and comparing them using the stoichiometry, we can find the limiting reactant.

Given that the reaction requires two moles of \( \mathrm{HNO}_3 \) for every mole of \( \mathrm{Mg(OH)}_2 \), a quick calculation shows that the amount of \( \mathrm{HNO}_3 \) present (0.005 mol) is not enough to react with all the \( \mathrm{Mg(OH)}_2 \) supplied (0.1329 mol). Thus, \( \mathrm{HNO}_3 \) is the limiting reactant.

An acid-base reaction is a chemical reaction that occurs between an acid and a base. In our exercise, \( \mathrm{HNO}_3 \), a known strong acid, reacts with \( \mathrm{Mg(OH)}_2 \), which acts as a base. The reaction results in the formation of magnesium nitrate \( \mathrm{Mg(NO}_3)_2 \) and water \( \mathrm{H}_2\mathrm{O} \).

These reactions are always characterized by the transfer of a proton (\( \mathrm{H}^+ \)) from the acid to the base. Here’s how this reaction can be understood:

• The nitric acid \( \mathrm{HNO}_3 \) donates \( \mathrm{H}^+ \) ions.
• The magnesium hydroxide \( \mathrm{Mg(OH)}_2 \), a base, accepts the \( \mathrm{H}^+ \) ions.
• This results in the formation of water molecules and a salt, in this case, magnesium nitrate.

Understanding these reactions is crucial because they form the basis of several processes, including titrations in analytical chemistry, and the production of various compounds in industrial reactions.

A balanced chemical equation is essential for understanding chemical reactions because it provides the correct proportionate amount of each reactant and product involved in the reaction.

In this case, balancing the equation helps us know how many moles of \( \mathrm{Mg(OH)}_2 \) and \( \mathrm{HNO}_3 \) are needed, and what products we get. The equation is:

• \( \mathrm{Mg(OH)}_2 + 2\mathrm{HNO}_3 \rightarrow \mathrm{Mg(NO}_3)_2 + 2\mathrm{H}_2\mathrm{O} \)

This equation is balanced because the number of atoms of each element is the same on both sides.

• 1 magnesium (Mg) atom is on both sides.
• 2 oxygen (O) atoms in \( \mathrm{Mg(OH)}_2 \) and 4 in 2\( \mathrm{HNO}_3 \), totalling 6 oxygens match perfectly with 4 in \( \mathrm{Mg(NO}_3)_2 \) and 2 in \( \mathrm{H}_2\mathrm{O} \).
• 4 hydrogen (H) atoms from 2\( \mathrm{HNO}_3 \) are balanced by 4 hydrogen atoms in 2 \( \mathrm{H}_2\mathrm{O} \).

Balancing is vital because it reflects the law of conservation of mass and ensures that calculations such as those for limiting reactants are accurate.