Question

Complete and balance each of the following single-replacement reactions: (a) \(\mathrm{Zn}(s)+\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q) \rightarrow\) (b) \(\mathrm{Cd}(s)+\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{2}(a q) \rightarrow\)

Short answer

(a) Balanced as: \(\text{Zn (s)} + \text{Pb(NO}_3\text{)}_2\text{ (aq)} \rightarrow \text{Zn(NO}_3\text{)}_2\text{ (aq)} + \text{Pb (s)}\); (b) Balanced as: \(\text{Cd (s)} + \text{Fe(NO}_3\text{)}_2\text{ (aq)} \rightarrow \text{Cd(NO}_3\text{)}_2\text{ (aq)} + \text{Fe (s)}\).

Step-by-step solution

Identify the Type of Reaction

The reactions given are single replacement reactions. In this type of reaction, an element reacts with a compound, and the element replaces another element in that compound.

Determine the Products for Reaction (a)

For reaction (a), since zinc (\(\text{Zn}\)) is more reactive than lead (Pb), it will replace lead in lead nitrate \(\text{Pb(NO}_3\text{)}_2\). This will form zinc nitrate \(\text{Zn(NO}_3\text{)}_2\) and lead metal \(\text{Pb}\). So, the equation becomes: \(\text{Zn (s)} + \text{Pb(NO}_3\text{)}_2\text{ (aq)} \rightarrow \text{Zn(NO}_3\text{)}_2\text{ (aq)} + \text{Pb (s)}\).

Balance the Equation for Reaction (a)

Check the number of atoms of each element on both the reactant and product sides. For every \(\text{Zn, Pb, N,}\) and \(\text{O}\) atom, the numbers are equal: 1 Zn, 1 Pb, 2 N, 6 O on both sides. This means the equation is already balanced.

Determine the Products for Reaction (b)

In reaction (b), since cadmium (\(\text{Cd}\)) is more reactive than iron \(\text{Fe}\), it will replace iron in iron nitrate \(\text{Fe(NO}_3\text{)}_2\). This will form cadmium nitrate \(\text{Cd(NO}_3\text{)}_2\) and iron metal \(\text{Fe}\). So, the equation becomes: \(\text{Cd (s)} + \text{Fe(NO}_3\text{)}_2\text{ (aq)} \rightarrow \text{Cd(NO}_3\text{)}_2\text{ (aq)} + \text{Fe (s)}\).

Balance the Equation for Reaction (b)

Check the number of atoms of each element. For both \(\text{Cd, Fe, N,}\) and \(\text{O}\) atoms, they are balanced: 1 Cd, 1 Fe, 2 N, 6 O on both sides. Thus, this equation is already balanced.

Key concepts

Single Replacement Reactions

In a single replacement reaction, one element moves into a compound and switches places with an element that is already part of that compound. This happens because some elements are more reactive or eager to form compounds than others. To figure out what will happen in these reactions, you need to know which element is more reactive. Generally, when a single replacement reaction occurs, you start by writing the reactants. For instance, element A reacts with compound BC to form AC and element B.

• **Element A replaces Element B**: If element A is more reactive than element B in compound BC, A will take B's place, forming AC and freeing B as a separate element.
• **Predicting the Products**: By knowing which element is more eager to react (or more reactive), we can easily predict the outputs of the reaction. For example, when zinc (Zn) reacts with lead nitrate, zinc is more reactive and replaces lead, forming zinc nitrate and freeing lead.

Balancing Chemical Equations

Balancing equations ensures that the same amount of each element is present both before and after a reaction. This is a fundamental principle of chemistry that stems from the law of conservation of mass. When you balance a chemical equation, every type of atom in the reactants must be accounted for in the same quantity among the products.

• **Count Atoms**: First, count the number of atoms of each element on both sides of the equation.
• **Adjust Coefficients, Not Subscripts**: To balance the equation, adjust the coefficients (the numbers before the compounds), but never alter the subscripts (the small numbers in the chemical formula itself). For example, if there are two oxygen atoms in the reactants and six oxygen atoms in the products, adjust the coefficients to balance them.
• **Iterate and Check**: Sometimes you may need to make several passes, adjusting coefficients repeatedly before the equation is balanced, such as in the reaction of cadmium (Cd) and iron nitrate, where balancing involves ensuring equal numbers of cadmium, iron, nitrogen, and oxygen atoms.

Reactivity Series

The reactivity series is a list of elements ordered by their ability to displace other elements in compounds, particularly metals. This list helps to predict the likelihood of a reaction occurring and can be a valuable tool for chemists.

• **Understanding Position**: If a metal is higher on the list, it means it is more reactive and more likely to displace another metal lower in the series. For example, zinc (Zn) is more reactive than lead (Pb), meaning it can replace lead in compounds like lead nitrate.
• **Predict Outcomes**: By using the reactivity series, you can predict the outcome of a chemical reaction before mixing the reactants. It provides a systematic approach to conducting experiments and understanding single replacement reactions.
• **Experimental Insights**: Knowledge of the reactivity series helps chemists make informed decisions in the lab, ensuring safety and precision in predicting what metals can replace others in chemical reactions without trial and error.