Question

Consider the unbalanced chemical equation. $$ \mathrm{Al}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{AlCl}_{3}(s) $$ A student tries to balance the equation by changing the subscript 2 on \(\mathrm{Cl}\) to a 3 . Explain why this is not correct. What is the correct balanced equation?

Short answer

The subscript in the chemical formula cannot be changed as it defines the compound. To balance the equation correctly, coefficients should be used instead: \[2\mathrm{Al}(s) + 3\mathrm{Cl}_2(g) \longrightarrow 2\mathrm{AlCl}_3(s)\].

Step-by-step solution

Understanding the Law of Conservation of Mass

The first principle to consider when balancing chemical equations is the Law of Conservation of Mass. This law states that matter cannot be created or destroyed in a chemical reaction, so the number of atoms of each element must be the same on both sides of the equation, though the arrangement of these atoms can change. Subscripts in a chemical formula represent the number of atoms in a molecule and cannot be changed to balance an equation because they define the substance. In contrast, coefficients are used to balance the equation, as they specify the number of molecules or moles of a substance.

Balancing Aluminum Atoms

Begin by looking at aluminum (Al) atoms. There is one Al atom on the reactant side and one Al atom in the product side (AlCl3). Since the Al atoms are already balanced, no further changes are needed for Al.

Balancing Chlorine Atoms

Next, look at the chlorine atoms. There are two Cl atoms on the reactant side (Cl2) and three Cl atoms on the product side (AlCl3). To balance the Cl atoms, we need to ensure the number of Cl atoms on both sides of the equation is the same.

Applying Coefficients to Balance Chlorine Atoms

To balance the Cl atoms, we adjust the coefficients, not the subscripts. By placing a coefficient of 3 in front of Cl2 on the reactant side and a coefficient of 2 in front of AlCl3 on the product side, we get 6 Cl atoms on both sides of the equation. The balanced chemical equation is: \[2\mathrm{Al}(s) + 3\mathrm{Cl}_2(g) \longrightarrow 2\mathrm{AlCl}_3(s)\]. This gives us 2 Al atoms and 6 Cl atoms on both sides of the equation.

Key concepts

Law of Conservation of Mass

The Law of Conservation of Mass is a fundamental principle in chemistry stating that during a chemical reaction, the total mass of the reactants must equal the total mass of the products. In other words, matter cannot be created or destroyed. This law forms the basis for balancing chemical equations, as it requires that the same number of each type of atom be present before and after the reaction.

For instance, if we start with atoms of aluminum (Al) and chlorine (Cl) reacting, no new aluminum or chlorine atoms can appear, nor can any disappear. Instead, atoms are rearranged into new compounds or molecules. This is crucial in understanding why we cannot arbitrarily change subscripts to balance equations, as doing so would imply that atoms are either being created or destroyed.

Chemical Equation Subscripts

Chemical equation subscripts play a pivotal role in dictating the composition of molecules in a chemical equation. A subscript is a small number written to the right of an atom in a chemical formula, and it indicates the number of atoms of that element in the molecule. For example, in the compound \(\mathrm{AlCl}_3\), the subscript '3' tells us there are three chlorine atoms for each aluminum atom in the molecule.

It is important to recognize that subscripts define the identity of a molecule and cannot be altered when balancing chemical equations. Changing a subscript would change the compound itself, which is not allowed under the Law of Conservation of Mass. Instead, we use coefficients to adjust the quantity of a substance without altering its identity.

Stoichiometry

Stoichiometry is the section of chemistry dealing with the quantitative relationships between the reactants and products in a chemical reaction. It is the calculation involving the masses or volumes of reactants and products. Stoichiometry utilizes the balanced chemical equation to determine the proportion in which substances react or are produced and to calculate the amounts required or formed in a reaction.

Understanding stoichiometry is essential for accurately determining the coefficients needed to balance a chemical equation. These coefficients indicate the ratios in which reactants combine and products form, ensuring that the number of atoms of each element is conserved, in accordance with the Law of Conservation of Mass. Coefficients give us the correct 'recipe' for a chemical reaction, just like proportions in a cooking recipe.

Chemical Reaction Coefficients

Chemical reaction coefficients are the numbers placed before molecules in a chemical equation, indicating the relative amounts of each substance that participates in the reaction. For example, in a balanced chemical equation, a coefficient of 2 in front of \(\mathrm{AlCl}_3\) means that two moles of aluminum chloride are produced.

Adjusting coefficients is the correct method to balance a chemical equation, ensuring that the Law of Conservation of Mass is obeyed. It is key to remember that while subscripts show the number of atoms within a single molecule, coefficients indicate the number of molecules, moles, or units of a substance. Changing coefficients adjusts the scale of the reaction but does not alter the actual identity of the compounds involved. Hence, coefficients are manipulated to balance an equation, reflecting the stoichiometry of the reaction.