Problem 6 - Chemistry Matter and Change

Question

$$ \mathrm{Mg}(\mathrm{s})+\mathrm{Pb}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Pb}(\mathrm{s})+\mathrm{Mg}^{2+}(\mathrm{aq}) $$

Step-by-Step Solution

Answer

The given chemical equation is already balanced: \(\mathrm{Mg}(\mathrm{s})+\mathrm{Pb}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Pb}(\mathrm{s})+\mathrm{Mg}^{2+}(\mathrm{aq})\). Since there is an equal number of each atom on both sides of the equation, no further steps are needed.

Step 1: Write the unbalanced equation

The given unbalanced chemical equation is: \[ \mathrm{Mg}(\mathrm{s})+\mathrm{Pb}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Pb}(\mathrm{s})+\mathrm{Mg}^{2+}(\mathrm{aq}) \]

Step 2: Identify the number of atoms of each element on both sides of the equation

Count the atoms of each element in reactants and products : Reactants: - Mg: 1 atom - Pb: 1 atom Products: - Pb: 1 atom - Mg: 1 atom

Step 3: Determine whether the equation is already balanced or not

Since there is an equal number of each atom on both sides of the equation, the given chemical equation is already balanced: \[ \mathrm{Mg}(\mathrm{s})+\mathrm{Pb}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Pb}(\mathrm{s})+\mathrm{Mg}^{2+}(\mathrm{aq}) \] This equation shows that one magnesium atom reacts with one lead ion to produce one lead atom and one magnesium ion. Since the number of atoms of each element is equal on both sides of the equation, no further steps are needed. The balanced chemical equation is: \[ \mathrm{Mg}(\mathrm{s})+\mathrm{Pb}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Pb}(\mathrm{s})+\mathrm{Mg}^{2+}(\mathrm{aq}) \]

Key Concepts

Chemical Reactions

A chemical reaction occurs when substances, known as reactants, transform into different substances, known as products. This transformation happens at a molecular level, requiring the breaking and forming of chemical bonds. Understanding chemical reactions is essential in explaining how elements and compounds interact with each other. These reactions can be classified into various types based on factors like the nature of the reactants, the direction of the change, and the energy changes involved. In our example above, magnesium and lead ions undergo a chemical reaction to form lead and magnesium ions. The reaction can be simply represented by the equation: \[ \mathrm{Mg} + \mathrm{Pb}^{2+} \rightarrow \mathrm{Pb} + \mathrm{Mg}^{2+} \]To maintain the reaction's requirement that atoms must be conserved, we write balanced equations. Balanced equations ensure that the number of atoms for each element is the same on the reactant and product sides. This principle stems from the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction, only rearranged.

Stoichiometry

Stoichiometry involves the calculation of quantitative relationships in a chemical reaction. It helps in predicting how much product will form from a certain amount of reactants or how much reactant is needed to form a desired amount of product.In the balanced equation given:\[ \mathrm{Mg}(\mathrm{s}) + \mathrm{Pb}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Pb}(\mathrm{s}) + \mathrm{Mg}^{2+}(\mathrm{aq}) \]we can determine the exact mole-to-mole relationship of reactants to products. One magnesium atom reacts with one lead ion. This 1:1 ratio reflects that stoichiometric coefficients, if used, would both be 1. Stoichiometry uses this concept to help understand the amounts required for reactions. It forms a crucial part in designing and scaling laboratory reactions and industrial processes, favoring efficiency and cost-effectiveness.

Oxidation-Reduction Reactions

Oxidation-reduction reactions, or redox reactions, are vital in chemistry because they involve the transfer of electrons between substances, resulting in changes to oxidation states. A classic hallmark of these reactions is the simultaneous occurrence of oxidation and reduction. In the equation:\[ \mathrm{Mg}(\mathrm{s}) + \mathrm{Pb}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Pb}(\mathrm{s}) + \mathrm{Mg}^{2+}(\mathrm{aq}) \]magnesium is oxidized, as it loses electrons to form \( \mathrm{Mg}^{2+} \). The magnesium starts with an oxidation state of 0 and ends with +2. Meanwhile, lead ion \( \mathrm{Pb}^{2+} \) is reduced as it gains electrons to form elemental lead with an oxidation state of 0. Understanding redox reactions is significant because they are integral to processes like combustion, respiration, and even industrial rusting prevention methods. Clarifying oxidation and reduction processes aids in mastering topics like electrochemistry and energy transfer.