Question

The balanced equation for the dissolving of magnesium nitrate in water is $$ \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}(s) \stackrel{\mathrm{H}, \mathrm{O}}{\longrightarrow} \mathrm{Mg}^{2+}(a q)+2 \mathrm{NO}_{3}{ }^{-}(a q) $$ (a) How many \(\mathrm{Mg}^{2+}(a q)\) and \(\mathrm{NO}_{3}(a q)\) ions form for each \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) formula unit that dissolves? (b) How many moles of \(\mathrm{Mg}^{2+}\) and \(\mathrm{NO}_{3}{ }^{-}\)form for each mole of \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) that dissolves?

Short answer

For each formula unit of \(Mg(NO_3)_2\) that dissolves, one \(Mg^{2+}\) and two \(NO_{3}\) ions are formed. Similarly, for each mole of \(Mg(NO_3)_2\) that dissolves, one mole of \(Mg^{2+}\) and two moles of \(NO_{3}^{-}\) are formed.

Step-by-step solution

Understanding the Balanced Equation

From the given balanced chemical equation, we can see that for every unit of \(Mg(NO_3)_2\), one \(Mg^{2+}\) and two \(NO_{3}^-\) ions are produced upon dissolution. This is the stoichiometry given directly by the balanced chemical equation.

Solution for sub-problem (a)

For each unit of \(Mg(NO_3)_2\), one \(Mg^{2+}\) ion is formed and two \(NO_{3}^-\) ions are formed based on the balanced chemical equation. This should answer the first query.

Solution for sub-problem (b)

On similar lines, since 'mole' is a counting unit for entities (like atoms, molecules, ions etc.), for one mole of \(Mg(NO_3)_2\) , one mole of \(Mg^{2+}\) and two moles of \(NO_{3}^-\) will be formed upon dissolving. This should answer the second query.

Key concepts

Chemical Stoichiometry

Chemical stoichiometry is a critical concept that allows us to predict the quantities of reactants and products involved in a chemical reaction. In essence, it's like a recipe for chemistry, providing the exact proportions needed to achieve a complete reaction without wasting any materials.

When we look at the reaction of magnesium nitrate dissolving in water, the stoichiometry tells us the ratio of magnesium ions to nitrate ions in the solution. This ratio is determined by the chemical formula of magnesium nitrate, \( Mg(NO_3)_2 \), and the balanced chemical equation. For each \( Mg(NO_3)_2 \) that dissolves, we obtain one \( Mg^{2+} \) ion and two \( NO_3^- \) ions, as indicated in the equation. This stoichiometric relationship is fundamental because it ensures that the dissolution process adheres to the law of conservation of mass, where no atoms are lost or gained, merely rearranged. This information is especially useful for practical applications like preparing solutions in a lab.

Balanced Chemical Equations

Balanced chemical equations are the backbone of many discussions in chemistry, providing insight into the relationships between reactants and products during reactions. Balancing equations is not just a formal exercise; it upholds the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction.

The equation for dissolving magnesium nitrate in water \( \mathrm{Mg}(\mathrm{NO}_{3})_{2}(s) \stackrel{\mathrm{H}_2\mathrm{O}}{\longrightarrow} \mathrm{Mg}^{2+}(aq) + 2 \mathrm{NO}_{3}^{-}(aq) \) is already balanced. It illustrates that one formula unit of solid magnesium nitrate yields one magnesium ion and two nitrate ions. It's crucial to approach the balancing of an equation methodically, ensuring that the same number of each type of atom appears on both sides of the equation. Understanding this concept helps predict the outcome of a reaction, making it essential for efficient and effective chemical synthesis.

Mole Concept

The mole concept is a foundational pillar in the study of chemistry, simplifying the way we measure substances. A mole is a unit that measures the amount of substance, analogous to how a dozen refers to twelve items. In chemistry, one mole represents Avogadro's number \( (6.022 \times 10^{23}) \) of entities, be it atoms, ions, or molecules.

For the dissolution of magnesium nitrate, when we talk about moles, we are referring to a very large number of formula units. If we were to dissolve one mole of \( Mg(NO_3)_2 \) in water, according to the balanced equation, it would result in the formation of one mole of \( Mg^{2+} \) ions and two moles of \( NO_3^- \) ions. This exemplifies the practical use of the mole concept, enabling chemists to work with macroscopic quantities of substances that are measurable and relatable to real-world laboratory scenarios.