Question

Write a balanced equation for each of the following single-replacement reactions: (a) Silver wire is put into a cadmium nitrate solution. (b) Cadmium wire is put into a silver nitrate solution.

Short answer

(a) No Reaction; (b) \( \text{Cd (s) + 2AgNO}_3\text{ (aq) } \rightarrow \text{Cd(NO}_3\text{)}_2\text{ (aq) + 2Ag (s)} \)

Step-by-step solution

Analyze Reaction (a)

In reaction (a), silver (Ag) is put into a cadmium nitrate solution. The chemical formula for cadmium nitrate is Cd(NO₃)₂. Silver is less reactive than cadmium, so no reaction will occur. Thus, silver cannot replace cadmium in cadmium nitrate. The equation remains unchanged: \[\text{Ag (s) + Cd(NO}_3\text{)}_2\text{ (aq) } \rightarrow \text{ No Reaction}\]

Analyze Reaction (b)

In reaction (b), cadmium (Cd) is put into a silver nitrate solution. The chemical formula for silver nitrate is AgNO₃. Cadmium is more reactive than silver and can replace silver in the compound, leading to the formation of cadmium nitrate and silver metal. The balanced equation is:\[\text{Cd (s) + 2AgNO}_3\text{ (aq) } \rightarrow \text{Cd(NO}_3\text{)}_2\text{ (aq) + 2Ag (s)}\]

Validate the Equation

Ensure that the chemical reactions are balanced. For reaction (b), count the atoms on both sides: - Cadmium: 1 (both reactant and product) - Silver: 2 in both silver nitrate and free silver - Nitrate: 2 in both sides This confirms that the equation for reaction (b) is balanced.

Key concepts

Chemical Equation Balancing

Balancing a chemical equation is essential for accurately representing a chemical reaction. It ensures that mass is conserved according to the law of conservation of matter. When balancing equations, each type of atom must have the same number on both the reactant and product sides. This ensures that no atoms are lost or gained during the reaction. Equations are balanced by adjusting coefficients, which are numbers placed in front of chemical formulas.
- First, identify the reactants and products in the reaction.- Count the number of atoms of each element present in the unbalanced equation.- Adjust the coefficients to get the same number of each type of atom on both sides.For example, in reaction (b), cadmium replaces silver in silver nitrate. The balanced equation is: \[\text{Cd (s) + 2AgNO}_3\text{ (aq) } \rightarrow \text{Cd(NO}_3\text{)}_2\text{ (aq) + 2Ag (s)}\]Here, the coefficient '2' in front of 'AgNO₃' and 'Ag' ensures that both sides have equal numbers of silver and nitrate ions.

Reactivity Series

The reactivity series is a crucial tool for predicting the outcome of single-replacement reactions. It orders metals by their ability to displace other metals from solutions of their ions. More reactive metals can replace less reactive ones. This series helps determine whether a specific reaction will occur.
Consider silver and cadmium: - Cadmium is higher in the reactivity series than silver. - This means cadmium can displace silver ions from a solution, forming cadmium nitrate. In reaction (b), cadmium replaces silver because it is more reactive, forming cadmium nitrate and silver metal: • Silver cannot replace cadmium in cadmium nitrate, as seen in reaction (a), because it is less reactive. Knowing the reactivity series allows chemists to predict if a reaction will occur and its products.

Silver Nitrate Solution

Silver nitrate (\( \text{AgNO}_3 \)) is a common chemical used in laboratory reactions. It dissolves in water, providing silver ions and nitrate ions. These ions can participate in chemical reactions, particularly single-replacement reactions.
- Silver ions (\( \text{Ag}^+ \)) can be displaced by more reactive metal ions.- Nitrate ions (\( \text{NO}_3^- \)) usually do not directly participate in the replacement.In reaction (b), silver nitrate reacts with cadmium:\[\text{Cd (s) + 2AgNO}_3\text{ (aq) } \rightarrow \text{Cd(NO}_3\text{)}_2\text{ (aq) + 2Ag (s)}\]The presence of silver nitrate leads to the formation of cadmium nitrate and metallic silver, showcasing its role in the chemical equation.

Cadmium Nitrate Solution

Cadmium nitrate (\( \text{Cd(NO}_3\text{)}_2 \)) is a chemical formed when silver is not reactive enough to replace cadmium in a solution, as shown in reaction (a). This compound consists of cadmium ions and nitrate ions dissolved in water.
- Cadmium ions (\( \text{Cd}^{2+} \)) remain in solution unless displaced by a more reactive metal.- Nitrate ions are typically spectator ions, not participating in the actual reactive process.In reaction (b), cadmium nitrate forms when cadmium displaces the less reactive silver, illustrating:\[\text{Cd (s) + 2AgNO}_3\text{ (aq) } \rightarrow \text{Cd(NO}_3\text{)}_2\text{ (aq) + 2Ag (s)}\]Understanding the chemistry of cadmium nitrate is valuable in predicting the outcomes of various metal replacement reactions.