Question

Balance each of the following skeletal equations: (a) \(\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{HCl}(a q) \longrightarrow \mathrm{AlCl}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) (b) \(\mathrm{PCl}_{3}(l)+\mathrm{AgF}(s) \longrightarrow \mathrm{PF}_{3}(g)+\mathrm{AgCl}(s)\) (c) \(\mathrm{NO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

Short answer

The balanced versions of each equation according to conservation of mass law are: (a) \( \mathrm{Al}_{2} \mathrm{O}_{3}(s) + 6\mathrm{HCl}(a q) \longrightarrow 2\mathrm{AlCl}_{3}(a q) + 3\mathrm{H}_{2} \mathrm{O}(l)\), (b) \(\mathrm{PCl}_{3}(l) + 3\mathrm{AgF}(s) \longrightarrow \mathrm{PF}_{3}(g) + 3\mathrm{AgCl}(s)\),(c) \(2\mathrm{NO}_{2}(g) \longrightarrow 2\mathrm{NO}(g) + \mathrm{O}_{2}(g)\).

Step-by-step solution

Balancing equation (a)

Starting with equation (a): \(\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{HCl}(a q) \longrightarrow \mathrm{AlCl}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\). The aluminium and chlorine atoms are already balanced but the oxygen and hydrogen are not. To balance the hydrogens, 6 molecules of \(\mathrm{HCl}\) are needed. To balance the oxygen, 3 water molecules are needed. The balanced equation therefore is: \( \mathrm{Al}_{2} \mathrm{O}_{3}(s) + 6\mathrm{HCl}(a q) \longrightarrow 2\mathrm{AlCl}_{3}(a q)+3\mathrm{H}_{2} \mathrm{O}(l)\)

Balancing equation (b)

Next, we consider equation (b): \(\mathrm{PCl}_{3}(l)+\mathrm{AgF}(s) \longrightarrow \mathrm{PF}_{3}(g)+\mathrm{AgCl}(s)\). The right hand side needs to have the same amounts of phosphorus, silver as the left hand side. As for chlorine, we need 3 chlorine atoms on the right to balance with the left ones, so 3 \(\mathrm{AgCl}\) formulas are needed. Lastly, for fluorine, we require 3 \(\mathrm{AgF}\) on the left side to balance with \(\mathrm{PF}_3\). The balanced equation thus reads: \(\mathrm{PCl}_{3}(l) + 3\mathrm{AgF}(s) \longrightarrow \mathrm{PF}_{3}(g) + 3\mathrm{AgCl}(s)\)

Balancing equation (c)

Finally, balancing equation (c): \(\mathrm{NO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) . The nitrogen atoms are already balanced but the oxygen are not. To balance the oxygens, 2 molecules of \(\mathrm{NO}_2\) are needed to produce 2 \(\mathrm{NO}\) molecules and 1 \(\mathrm{O}_{2}\) molecule. The balanced equation becomes: \(2\mathrm{NO}_{2}(g) \longrightarrow 2\mathrm{NO}(g)+\mathrm{O}_{2}(g)\).

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. At the heart of stoichiometry lies the Law of Conservation of Mass, which states that in a chemical reaction, mass is neither created nor destroyed. This principle implies that the mass of the reactants must equal the mass of the products, which is why chemical equations must be balanced.
Stoichiometric calculations involve using the coefficients of a balanced equation to calculate the amounts of reactants needed or products formed. For example, in an exercise to balance the reaction between aluminum oxide and hydrochloric acid to form aluminum chloride and water, you’re essentially determining the relative amounts of each compound that react according to the stoichiometry of the equation. By understanding stoichiometry, students can predict the yield of a reaction, how much of each reactant is required, or how much of a product will be formed from given quantities of reactants.

• Law of Conservation of Mass as a foundation.
• Use of balanced equations for quantitative predictions.
• Understanding reactant-product relationships.

Chemical Reactions

A chemical reaction involves the transformation of one or more substances, known as reactants, into different substances, called products. These transformations occur as a result of the breaking and forming of chemical bonds. Chemical reactions are described using chemical equations that give information about the reactants and products involved, as well as their physical states, such as solid (s), liquid (l), gaseous (g), or aqueous (aq).
Recognizing the type of chemical reaction occurring can aid in the balancing process. There are several basic types of reactions, such as synthesis, decomposition, single replacement, double replacement, and combustion. For instance, the reaction between nitrogen dioxide and oxygen to form nitrogen monoxide and oxygen gas is a decomposition reaction, where a more complex molecule breaks down into simpler ones. Understanding the types of chemical reactions helps in predicting the products that might form and provides clues for balancing the equation correctly.

• Transformation of reactants to products.
• Identification of physical states in a chemical equation.
• Recognition of different types of chemical reactions for aiding the balancing process.

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry, crucial for correctly describing a chemical reaction. It involves writing an equation so that the same number of each type of atom appears on both the reactant and product sides, adhering to the Law of Conservation of Mass.
To balance a chemical equation, like the reaction between phosphorus trichloride and silver fluoride to form phosphorus trifluoride and silver chloride, you need to adjust the coefficients—the numbers in front of compounds—to ensure the same number of each atom on both sides. The exercise provided illustrates the process step-by-step, showing the importance of adjusting coefficients methodically. It’s essential to balance each element one at a time and to avoid altering chemical formulas of the reactants and products.
Improving your skills in balancing equations requires practice, attention to detail, and a systematic approach:

• Maintaining the correct stoichiometry of compounds.
• Iteratively adjusting coefficients to balance each element.
• Confirming the mass balance for the complete equation.

An understanding of the steps involved can give students the confidence needed to tackle even the most complex chemical equations.