Question

Explain why the equivalent weight of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is half the molar mass of this substance. How many hydrogen ions does each \(\mathrm{H}_{2} \mathrm{SO}_{4}\) molecule produce when reacting with an excess of \(\mathrm{OH}^{-}\) ions?

Short answer

The equivalent weight of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) is half its molar mass because it is a diprotic acid, meaning it can lose two hydrogen ions (\(\mathrm{H}^+\)) per molecule when reacting. This is represented by the chemical equation \(\mathrm{H}_{2}\mathrm{SO}_{4} \rightarrow 2\mathrm{H}^{+}+\mathrm{SO}_{4}^{2-}\). Thus, each \(\mathrm{H}_{2}\mathrm{SO}_{4}\) molecule produces \(2\) hydrogen ions when reacting with an excess of \(\mathrm{OH}^-\) ions.

Step-by-step solution

1. Equivalent Weight and Molar Mass Relation for \(\mathrm{H}_{2}\mathrm{SO}_{4}\)

The molar mass of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) can be calculated by adding the molar mass of all atoms present in the molecule: \[M_\text{H2SO4} = 2(\text{M}_\mathrm{H})+(\text{M}_\mathrm{S})+4(\text{M}_\mathrm{O})\] Now, we can determine the equivalent weight. The equivalent weight of an acid is the mass of the acid required to produce one mole of hydrogen ions (\(\mathrm{H}^+\)) or, equivalently, the mass required to neutralize one mole of \(\mathrm{OH}^-\) hydroxide ions. Sulfuric acid \(\mathrm{(H_{2}SO_{4})}\) is a diprotic acid, meaning it can lose two hydrogen ions (\(\mathrm{H}^+\)) when it reacts, as shown in the chemical equation: \[\mathrm{H}_{2}\mathrm{SO}_{4} \rightarrow 2\mathrm{H}^{+}+\mathrm{SO}_{4}^{2-}\] Since \(\mathrm{H}_{2}\mathrm{SO}_{4}\) releases two moles of \(\mathrm{H}^+\) ions per mole of the acid, its equivalent weight will be half its molar weight: \[\frac{M_\text{H2SO4}}{2} = \text{Equivalent Weight}\]

2. Determining the Number of Hydrogen Ions Produced by an \(\mathrm{H}_{2}\mathrm{SO}_{4}\) Molecule

When an \(\mathrm{H}_{2}\mathrm{SO}_{4}\) molecule reacts with an excess of hydroxide ions, each molecule can produce hydrogen ions. The diprotic nature of the sulfuric acid tells us that each molecule will release two hydrogen ions, as shown in the chemical equation we derived earlier: \[\mathrm{H}_{2}\mathrm{SO}_{4} \rightarrow 2\mathrm{H}^{+}+\mathrm{SO}_{4}^{2-}\] Therefore, each \(\mathrm{H}_{2}\mathrm{SO}_{4}\) molecule produces \(2\) hydrogen ions when reacting with an excess of \(\mathrm{OH}^-\) ions.