Question

Balance each of the following equations that describe decomposition reactions. a. \(\mathrm{NaHCO}_{3}(s) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}_{2}(g)\) b. \(\mathrm{NaClO}_{3}(s) \rightarrow \mathrm{NaCl}(s)+\mathrm{O}_{2}(g)\) c. \(\mathrm{HgO}(s) \rightarrow \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\) d. \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s) \rightarrow \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) e. \(\mathrm{H}_{2} \mathrm{O}_{2}(l) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)\)

Short answer

The balanced decomposition reactions are: a. \(2 NaHCO_{3}(s) \rightarrow Na_{2}CO_{3}(s) + H_{2}O(g) + CO_{2}(g)\) b. \(2 NaClO_{3}(s) \rightarrow 2 NaCl(s) + 3 O_{2}(g)\) c. \(2 HgO(s) \rightarrow 2 Hg(l) + O_{2}(g)\) d. \(C_{12}H_{22}O_{11}(s) \rightarrow 12 C(s) + 11 H_{2}O(g)\) e. \(2 H_{2}O_{2}(l) \rightarrow 2 H_{2}O(l) + O_{2}(g)\)

Step-by-step solution

(Balancing equation a)

\(NaHCO_{3}(s) \rightarrow Na_{2}CO_{3}(s) + H_{2}O(g) + CO_{2}(g)\) 1. List the number of atoms for each element on both sides: \ Reactant side: Na=1, H=1, C=1, O=3 \ Product side: Na=2, H=2, C=2, O=5 2. Balance the equation by adjusting coefficients: \[2 NaHCO_{3}(s) \rightarrow Na_{2}CO_{3}(s) + H_{2}O(g) + CO_{2}(g)\] Now, we have: Na=2, H=2, C=2, and O=6 on both sides.

(Balancing equation b)

\(NaClO_{3}(s) \rightarrow NaCl(s) + O_{2}(g)\) 1. List the number of atoms for each element on both sides: \ Reactant side: Na=1, Cl=1, O=3 \ Product side: Na=1, Cl=1, O=2 2. Balance the equation by adjusting coefficients: \[2 NaClO_{3}(s) \rightarrow 2 NaCl(s) + 3 O_{2}(g)\] Now, we have: Na=2, Cl=2, and O=6 on both sides.

(Balancing equation c)

\(HgO(s) \rightarrow Hg(l) + O_{2}(g)\) 1. List the number of atoms for each element on both sides: \ Reactant side: Hg=1, O=1 \ Product side: Hg=1, O=2 2. Balance the equation by adjusting coefficients: \[2 HgO(s) \rightarrow 2 Hg(l) + O_{2}(g)\] Now, we have: Hg=2, and O=2 on both sides.

(Balancing equation d)

\(C_{12}H_{22}O_{11}(s) \rightarrow C(s) + H_{2}O(g)\) 1. List the number of atoms for each element on both sides: \ Reactant side: C=12, H=22, O=11 \ Product side: C=1, H=2, O=1 2. Balance the equation by adjusting coefficients: \[C_{12}H_{22}O_{11}(s) \rightarrow 12 C(s) + 11 H_{2}O(g)\] Now, we have: C=12, H=22, and O=11 on both sides.

(Balancing equation e)

\(H_{2}O_{2}(l) \rightarrow H_{2}O(l) + O_{2}(g)\) 1. List the number of atoms for each element on both sides: \ Reactant side: H=2, O=2 \ Product side: H=2, O=3 2. Balance the equation by adjusting coefficients: \[2 H_{2}O_{2}(l) \rightarrow 2 H_{2}O(l) + O_{2}(g)\] Now, we have: H=4, and O=4 on both sides.

Key concepts

Decomposition Reactions

A decomposition reaction is a type of chemical reaction in which a single compound breaks down into two or more simple substances. This can include elements or less complex compounds. Decomposition reactions generally require energy in the form of heat, light, or electricity to occur. They are crucial in various industrial processes as well as natural occurrences. For example, the decomposition of hydrogen peroxide into water and oxygen is used in various cleaning and disinfection processes. Recognizing decomposition reactions is straightforward: you start with one reactant and end with multiple products.

Reactant and Product Atoms

The balance of atoms from reactants to products is central in all chemical reactions, including decomposition reactions. This follows the law of conservation of mass, which states that matter is neither created nor destroyed. Therefore, the number of each type of atom must remain consistent on both sides of a balanced chemical equation.
In the context of a decomposition reaction, you begin with the reactants, where the atoms of these substances are accounted for. Then, by breaking down the compounds into products, you ensure that each element's atom count on the reactant side equals the atom count on the product side, maintaining balance and respecting the laws of chemistry.

Chemical Equation Coefficients

Chemical equation coefficients are numbers placed before compounds in an equation to indicate the number of units of each substance involved in a reaction. Adjusting these coefficients is the primary method used to balance chemical equations. Instead of changing the subscripts of the formulas (which would change their identities), altering the coefficients adjusts the quantities while maintaining the integrity of the compounds involved.
For instance, if \( \text{NaClO}_3 \rightarrow \text{NaCl} + \text{O}_2 \) is unbalanced due to differing oxygen atoms, the solution is updating coefficients to ensure equal amounts of each element on both sides of the equation, resulting in balanced reactants and products.

Chemical Balancing Steps

Balancing chemical equations involves several structured steps to ensure accuracy. First, list all atoms of each element present in the reactants and products. Next, usually starting with the most complex molecule, adjust the coefficients to aim for equal numbers of each type of atom on both sides of the equation.
Additional tips include balancing polyatomic ions as a single unit if they appear unchanged on both sides, and saving oxygen and hydrogen for last, as they are often more prevalent. Finally, double-check your equation by recounting the atoms, ensuring complete parity between reactants and products. Mastering these steps ensures a properly balanced chemical equation, critical in both theoretical and practical chemistry applications.