Problem 5 - Chemistry and Chemical Reactivity

Question

Balance the following equations, and name each reactant and product: (a) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+\mathrm{Mg}(\mathrm{s}) \rightarrow \mathrm{MgO}(\mathrm{s})+\mathrm{Fe}(\mathrm{s})\) (b) \(\mathrm{AlCl}_{3}(\mathrm{s})+\mathrm{NaOH}(\mathrm{aq}) \rightarrow \mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})+\mathrm{NaCl}(\mathrm{aq})\) (c) \(\mathrm{NaNO}_{3}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{s})+\mathrm{HNO}_{3}(\mathrm{aq})\) (d) \(\mathrm{NiCO}_{3}(\mathrm{s})+\mathrm{HNO}_{3}(\mathrm{aq}) \rightarrow \mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell)\)

Step-by-Step Solution

Answer

(a) \( \mathrm{Fe}_2\mathrm{O}_3 + 3\mathrm{Mg} \rightarrow 3\mathrm{MgO} + 2\mathrm{Fe} \); (b) \( \mathrm{AlCl}_3 + 3\mathrm{NaOH} \rightarrow \mathrm{Al(OH)}_3 + 3\mathrm{NaCl} \); (c) \( 2\mathrm{NaNO}_3 + \mathrm{H}_2\mathrm{SO}_4 \rightarrow \mathrm{Na}_2\mathrm{SO}_4 + 2\mathrm{HNO}_3 \); (d) \( \mathrm{NiCO}_3 + 2\mathrm{HNO}_3 \rightarrow \mathrm{Ni(NO}_3)_2 + \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \).

Step 1: Understand the Problem

We need to balance four chemical equations and identify each reactant and product. Balancing involves making sure that the same number of each type of atom appears on both sides of the equation.

Step 2: Equation (a) Identification

Identify and name each substance in the equation: \( \mathrm{Fe}_2\mathrm{O}_3 \) (Iron(III) oxide), \( \mathrm{Mg} \) (Magnesium), \( \mathrm{MgO} \) (Magnesium oxide), and \( \mathrm{Fe} \) (Iron).

Step 3: Balance Equation (a)

Balance the equation by adjusting coefficients. The balanced equation is: \( \mathrm{Fe}_2\mathrm{O}_3 + 3\mathrm{Mg} \rightarrow 3\mathrm{MgO} + 2\mathrm{Fe} \). Check by counting atoms: 2 Fe, 3 O, and 3 Mg on both sides.

Step 4: Equation (b) Identification

Identify and name each substance in the equation: \( \mathrm{AlCl}_3 \) (Aluminum chloride), \( \mathrm{NaOH} \) (Sodium hydroxide), \( \mathrm{Al(OH)}_3 \) (Aluminum hydroxide), \( \mathrm{NaCl} \) (Sodium chloride).

Step 5: Balance Equation (b)

Balance the equation: \( \mathrm{AlCl}_3 + 3\mathrm{NaOH} \rightarrow \mathrm{Al(OH)}_3 + 3\mathrm{NaCl} \). Verify: 1 Al, 3 Cl, 3 Na, and 3 OH groups are balanced.

Step 6: Equation (c) Identification

Identify and name each substance in the equation: \( \mathrm{NaNO}_3 \) (Sodium nitrate), \( \mathrm{H}_2\mathrm{SO}_4 \) (Sulfuric acid), \( \mathrm{Na}_2\mathrm{SO}_4 \) (Sodium sulfate), \( \mathrm{HNO}_3 \) (Nitric acid).

Step 7: Balance Equation (c)

The balanced equation is: \( 2\mathrm{NaNO}_3 + \mathrm{H}_2\mathrm{SO}_4 \rightarrow \mathrm{Na}_2\mathrm{SO}_4 + 2\mathrm{HNO}_3 \). Check: 2 Na, 2 N, 6 O for nitrates, 2 H, 1 S, and 4 O for sulfate.

Step 8: Equation (d) Identification

Identify and name each substance in the equation: \( \mathrm{NiCO}_3 \) (Nickel(II) carbonate), \( \mathrm{HNO}_3 \) (Nitric acid), \( \mathrm{Ni(NO}_3)_{2} \) (Nickel(II) nitrate), \( \mathrm{CO}_2 \) (Carbon dioxide), \( \mathrm{H}_2\mathrm{O} \) (Water).

Step 9: Balance Equation (d)

The balanced equation is: \( \mathrm{NiCO}_3 + 2\mathrm{HNO}_3 \rightarrow \mathrm{Ni(NO}_3)_2 + \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \). Verify: 1 Ni, 1 C, 3 O for carbonate, 2 N, 6 O for nitrates, 2 H, and 1 O for water.

Key Concepts

Reactants and Products

In chemical reactions, we deal with reactants and products. Reactants are the starting substances that undergo change, while products are the new substances formed as a result of the reaction. Understanding the role of each component is crucial for balancing equations correctly.

Consider the reaction of iron(III) oxide with magnesium: \( \mathrm{Fe}_2\mathrm{O}_3 + 3\mathrm{Mg} \rightarrow 3\mathrm{MgO} + 2\mathrm{Fe} \).

• **Reactants**: Iron(III) oxide (\( \mathrm{Fe}_2\mathrm{O}_3 \)), Magnesium (\( \mathrm{Mg} \))
• **Products**: Magnesium oxide (\( \mathrm{MgO} \)), Iron (\( \mathrm{Fe} \))

This equation features two reactants combining to form two distinct products.Another example is the reaction: \( \mathrm{AlCl}_3 + 3\mathrm{NaOH} \rightarrow \mathrm{Al(OH)}_3 + 3\mathrm{NaCl} \).

• **Reactants**: Aluminum chloride (\( \mathrm{AlCl}_3 \)), Sodium hydroxide (\( \mathrm{NaOH} \))
• **Products**: Aluminum hydroxide (\( \mathrm{Al(OH)}_3 \)), Sodium chloride (\( \mathrm{NaCl} \))

In this case, the reactants interact to produce compounds with different compositions and properties.

Chemical Nomenclature

Chemical nomenclature is the system used to name chemical substances. It's important because accurate names help us identify the compounds involved in reactions. Let’s explore some examples from the equations we're working with:

Iron(III) oxide (\( \mathrm{Fe}_2\mathrm{O}_3 \)) tells us it's an oxide of iron in the +3 oxidation state, indicated by "III".
Magnesium oxide (\( \mathrm{MgO} \)) shows magnesium has combined with oxygen.

In the equation \( \mathrm{AlCl}_3 + 3\mathrm{NaOH} \rightarrow \mathrm{Al(OH)}_3 + 3\mathrm{NaCl} \):

• **Aluminum chloride** (\( \mathrm{AlCl}_3 \)) combines aluminum with chlorine.
• **Sodium chloride** (\( \mathrm{NaCl} \)) consists of sodium and chlorine, commonly known as table salt.

Correctly identifying these names helps in checking the reaction equations and balancing them.
Always pay attention to chemical formulas as they reveal the types and quantities of atoms involved.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It's the method used to ensure atoms on both sides of a chemical equation are equal, maintaining the law of conservation of mass.

When balancing equations, we alter coefficients, not subscripts. Coefficients apply to the whole compound, while subscripts only to individual elements within the compound.

For example, balancing the equation \(\mathrm{Fe}_2\mathrm{O}_3 + 3\mathrm{Mg} \rightarrow 3\mathrm{MgO} + 2\mathrm{Fe}\) requires:

• 2 iron atoms are on both sides.
• 3 magnesium atoms react to form 3 magnesium oxide molecules.

This balancing process illustrates stoichiometry at work.

Similarly, to balance \(\mathrm{AlCl}_3 + 3\mathrm{NaOH} \rightarrow \mathrm{Al(OH)}_3 + 3\mathrm{NaCl}\), we adjust coefficients so that:

• 1 aluminum and 3 chlorine, sodium, and hydroxide ions are present on both sides.

By keeping the atom count equal on both sides, we maintain the equation's integrity and accuracy.