Question

Complete and balance the equations for the following double-displacement reactions: a. \(\operatorname{AgNO}_{3}(a q)+\operatorname{NaCl}(a q) \longrightarrow\) ________ b. \(\operatorname{Mg}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{KOH}(a q) \longrightarrow\) ________ c. \(\operatorname{LiOH}(a q)+\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}(a q) \longrightarrow\) ________

Short answer

a. \(\text{AgNO}_3 (aq) + \text{NaCl} (aq) \rightarrow \text{AgCl} (s) + \text{NaNO}_3 (aq)\) b. \(\text{Mg(NO}_3\text{)_2} (aq) + \text{2 KOH} (aq) \rightarrow \text{Mg(OH)}_2 (s) + \text{2 KNO}_3 (aq)\) c. \(\text{3 LiOH} (aq) + \text{Fe(NO}_3\text{)_3} (aq) \rightarrow \text{Fe(OH)}_3 (s) + \text{3 LiNO}_3 (aq)\)

Step-by-step solution

Title - Identify the products for each reaction

In a double-displacement reaction, the cations and anions of the reactants switch places. For the given reactions: a. \(\text{AgNO}_3 (aq) + \text{NaCl} (aq) \rightarrow \text{AgCl} (s) + \text{NaNO}_3 (aq)\) b. \(\text{Mg(NO}_3\text{)_2} (aq) + \text{KOH} (aq) \rightarrow \text{Mg(OH)}_2 (s) + \text{KNO}_3 (aq)\) c. \(\text{LiOH} (aq) + \text{Fe(NO}_3\text{)_3} (aq) \rightarrow \text{Fe(OH)}_3 (s) + \text{LiNO}_3 (aq)\)

Title - Balance Equation (a)

Equation (a) is \(\text{AgNO}_3 (aq) + \text{NaCl} (aq) \rightarrow \text{AgCl} (s) + \text{NaNO}_3 (aq)\). It is already balanced as each side has one atom of Ag, one atom of Na, one atom of Cl, and one NO3 group.

Title - Balance Equation (b)

Equation (b) is \(\text{Mg(NO}_3\text{)_2} (aq) + \text{2 KOH} (aq) \rightarrow \text{Mg(OH)}_2 (s) + \text{2 KNO}_3 (aq)\). It is balanced by ensuring that both sides have one atom of Mg, two atoms of OH, and two NO3 groups.

Title - Balance Equation (c)

Equation (c) is \(\text{3 LiOH} (aq) + \text{Fe(NO}_3\text{)_3} (aq) \rightarrow \text{Fe(OH)}_3 (s) + \text{3 LiNO}_3 (aq)\). It is balanced by making sure there are three Li atoms and three OH groups on both sides.

Key concepts

chemical reactions

A chemical reaction occurs when substances, known as reactants, transform into other substances called products. There are several types of chemical reactions, and one common type is the double-displacement reaction. In a double-displacement reaction, two compounds exchange ions to form two new compounds. It's essential to identify the reactants and predict the products by switching the cations and anions.

In the given exercise, we see typical examples of double-displacement reactions:

- \(\text{AgNO}_3 (aq) + \text{NaCl} (aq) \rightarrow \text{AgCl} (s) + \text{NaNO}_3 (aq)\)
- \(\text{Mg(NO}_3\text{)_2} (aq) + \text{KOH} (aq) \rightarrow \text{Mg(OH)}_2 (s) + \text{KNO}_3 (aq)\)
- \(\text{LiOH} (aq) + \text{Fe(NO}_3\text{)_3} (aq) \rightarrow \text{Fe(OH)}_3 (s) + \text{LiNO}_3 (aq)\)

Notice how the compounds on the left side of the equation exchange parts to form new compounds on the right side. This process demonstrates how ions rearrange themselves during a chemical reaction, leading to the formation of new products.

balancing equations

Balancing chemical equations is crucial to obey the Law of Conservation of Mass, which states that matter cannot be created or destroyed. This implies that the number of atoms for each element must be the same on both sides of the equation.

Take reaction (a) as an example: \(\text{AgNO}_3 (aq) + \text{NaCl} (aq) \rightarrow \text{AgCl} (s) + \text{NaNO}_3 (aq)\). This equation is already balanced because:

• One silver (Ag) atom on both sides
• One chlorine (Cl) atom on both sides
• One sodium (Na) atom on both sides
• One nitrate (NO3) group on both sides

Equation (b), however, needed adjustment: \(\text{Mg(NO}_3\text{)_2} (aq) + \text{KOH} (aq) \rightarrow \text{Mg(OH)}_2 (s) + \text{KNO}_3 (aq)\). By adding a coefficient of 2 for KOH and KNO3, it balances:

• One magnesium (Mg) atom
• Two hydroxide (OH) groups
• Two nitrate (NO3) groups

Lastly, equation (c) required balancing too: \(\text{LiOH} (aq) + \text{Fe(NO}_3\text{)_3} (aq) \rightarrow \text{Fe(OH)}_3 (s) + \text{LiNO}_3 (aq)\). By using a coefficient of 3 for LiOH and LiNO3, it balances:

• Three lithium (Li) atoms
• Three hydroxide (OH) groups

By ensuring that the number of atoms is balanced on both sides, we respect fundamental chemical principles and can accurately describe the reactions.

reaction products

In a double-displacement reaction, identifying the reaction products is straightforward once you understand how the cations and anions switch places. Let's explore the specific products of the reactions:

- \( \text{AgNO}_3 (aq) + \text{NaCl} (aq) \rightarrow \text{AgCl} (s) + \text{NaNO}_3 (aq) \): Silver nitrate and sodium chloride react to form silver chloride, which is a solid (precipitate), and sodium nitrate, which remains in solution.
- \( \text{Mg(NO}_3\text{)_2} (aq) + \text{KOH} (aq) \rightarrow \text{Mg(OH)}_2 (s) + \text{KNO}_3 (aq) \): Magnesium nitrate reacts with potassium hydroxide to form magnesium hydroxide, which precipitates out, and potassium nitrate, which stays dissolved.
- \( \text{LiOH} (aq) + \text{Fe(NO}_3\text{)_3} (aq) \rightarrow \text{Fe(OH)}_3 (s) + \text{LiNO}_3 (aq) \): Lithium hydroxide reacts with iron(III) nitrate to produce iron(III) hydroxide, a solid precipitate, and lithium nitrate, an aqueous product.

Understanding the nature of the products helps in predicting whether a precipitate will form, which is a visible sign of the chemical reaction occurring. Additionally, recognizing the products helps in further chemical analysis and applying the knowledge to real-world chemical processes.