How many moles of \(\mathrm{Ba}(\mathrm{OH})_{2}\) does it take to neutralize \(0.50\) mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) ? Why does the resulting solution after the neutralization no longer conduct electricity? Why does the solution then conduct electricity after an excess of \(\mathrm{Ba}(\mathrm{OH})_{2}\) is added?

Balancing a chemical equation is a foundational skill in chemistry. It involves making sure that the number of atoms of each element is the same on both sides of the equation, abiding by the Law of Conservation of Mass. For example, the balanced chemical equation for the neutralization reaction between barium hydroxide and sulfuric acid is:
\[\begin{equation}\mathrm{Ba}(\mathrm{OH})_{2} + \mathrm{H}_{2}\mathrm{SO}_{4} \rightarrow \mathrm{BaSO}_{4} + 2 \mathrm{H}_{2}\mathrm{O}.\end{equation}\]
In this equation, we have one barium atom, two hydroxide groups, one sulfur atom and four oxygen atoms on both sides, ensuring the balance. This process allows us to understand the stoichiometry of the reaction and predict the quantities of reactants and products involved.

Stoichiometric calculations are used to compute the amounts of reactants and products in a chemical reaction. Based on the moles of substances involved, these calculations rely on the balanced chemical equation. For instance, the neutralization reaction we're examining tells us that one mole of \[\begin{equation}\mathrm{Ba}(\mathrm{OH})_{2}\end{equation}\]reacts with one mole of \[\begin{equation}\mathrm{H}_{2}\mathrm{SO}_{4}.\end{equation}\]Therefore, to neutralize 0.50 mole of sulfuric acid, we would need 0.50 mole of barium hydroxide. Understanding stoichiometry is essential for predicting how much of each substance will be needed or produced in a reaction.

Electrolytic conductivity refers to the ability of a solution to conduct electricity due to the presence of free ions. In a neutralization reaction, such as the one between barium hydroxide and sulfuric acid, the resulting solution no longer conducts electricity because it forms water and a precipitate of barium sulfate. Both products do not release ions into the solution.

Importance of Free Ions

Without free ions, there are no charge carriers, and the solution's ability to conduct electricity diminishes. Adding an excess of barium hydroxide reintroduces free barium and hydroxide ions, allowing the solution to conduct electricity once again.

The mole concept is a central theme in chemistry that relates the mass of substances to the number of particles contained within them. One mole is defined as exactly 6.02214076 \times 10^{23} (Avogadro's number) of particles (atoms, molecules, ions, etc.).

Applying the Mole Concept

For the neutralization reaction problem, when it states '0.50 mole of \[\begin{equation}\mathrm{H}_{2}\mathrm{SO}_{4}\end{equation}\], it refers to 0.50 times Avogadro's number of sulfuric acid molecules. The mole concept allows chemists to count substances in the laboratory and convert between mass and number of particles for chemical reactions.