Question

Balance each of the following chemical equations by inspection: (a) \(\mathrm{FeO}(l)+\mathrm{Al}(l) \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(l)+\mathrm{Fe}(l)\) (b) \(\mathrm{MnO}_{2}(l)+\mathrm{Al}(l) \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(l)+\mathrm{Mn}(l)\)

Short answer

(a) The balanced equation is: \[ 3\mathrm{FeO} + 2\mathrm{Al} \rightarrow \mathrm{Al}_{2}\mathrm{O}_{3} + 3\mathrm{Fe} \]. (b) The balanced equation is: \[ 3\mathrm{MnO}_{2} + 4\mathrm{Al} \rightarrow 2\mathrm{Al}_{2}\mathrm{O}_{3} + 3\mathrm{Mn} \].

Step-by-step solution

Write the Unbalanced Equation for Reaction (a)

The unbalanced chemical equation given is:\[ \mathrm{FeO}(l)+\mathrm{Al}(l) \rightarrow \mathrm{Al}_{2}\mathrm{O}_{3}(l)+\mathrm{Fe}(l) \]

Balance the Aluminum Atoms for Reaction (a)

There are 2 aluminum atoms in \( \mathrm{Al}_{2}\mathrm{O}_{3} \) on the right side, so we place a coefficient of 2 in front of \( \mathrm{Al} \) on the left side to balance aluminum:\[ \mathrm{FeO}(l) + 2\mathrm{Al}(l) \rightarrow \mathrm{Al}_{2}\mathrm{O}_{3}(l) + \mathrm{Fe}(l) \]

Balance Iron and Oxygen Atoms for Reaction (a)

There are no oxygen atoms in the products aside from those in \( \mathrm{Al}_{2}\mathrm{O}_{3} \), so let's balance the iron atoms next. Place a coefficient of 3 in front of \( \mathrm{FeO} \) and 3 in front of \( \mathrm{Fe} \) to balance the iron and keep the oxygen balanced:\[ 3\mathrm{FeO}(l) + 2\mathrm{Al}(l) \rightarrow \mathrm{Al}_{2}\mathrm{O}_{3}(l) + 3\mathrm{Fe}(l) \]

Write the Unbalanced Equation for Reaction (b)

The unbalanced chemical equation given is:\[ \mathrm{MnO}_{2}(l)+\mathrm{Al}(l) \rightarrow \mathrm{Al}_{2}\mathrm{O}_{3}(l)+\mathrm{Mn}(l) \]

Balance the Aluminum Atoms for Reaction (b)

There are 2 aluminum atoms in \( \mathrm{Al}_{2}\mathrm{O}_{3} \) on the right side, so place a coefficient of 2 in front of \( \mathrm{Al} \) on the left side to balance aluminum:\[ \mathrm{MnO}_{2}(l) + 2\mathrm{Al}(l) \rightarrow \mathrm{Al}_{2}\mathrm{O}_{3}(l) + \mathrm{Mn}(l) \]

Balance Manganese and Oxygen Atoms for Reaction (b)

To balance oxygen, we notice the discrepancy in the number of oxygen atoms on each side. The left side has 2 oxygen in \( \mathrm{MnO}_{2} \) and the right side has 3 oxygen in \( \mathrm{Al}_{2}\mathrm{O}_{3} \). Adding a coefficient of 3 to \( \mathrm{MnO}_{2} \) and checking the other elements, corrects the imbalance, however, we need to also update \( \mathrm{Mn} \):\[ 3\mathrm{MnO}_{2}(l) + 4\mathrm{Al}(l) \rightarrow 2\mathrm{Al}_{2}\mathrm{O}_{3}(l) + 3\mathrm{Mn}(l) \]

Verify the Balanced Equations

For Reaction (a), check that there are equal numbers of each type of atom on both sides: 3 Fe and 3 O on both sides, and 2 Al on both sides. For Reaction (b), 3 Mn, 4 Al, and 6 O exist on both sides, confirming balance.

Key concepts

Stoichiometry

Stoichiometry plays a critical role in understanding chemical reactions by helping us know how much of each substance is needed or produced. It involves using balanced chemical equations to determine the relative amounts of reactants and products involved in a reaction. This means that during a reaction, substances may change form, but the overall quantity of atoms involved remains constant.
Let's dive into an example with reaction (a):\[3\mathrm{FeO}(l) + 2\mathrm{Al}(l) \rightarrow \mathrm{Al}_{2}\mathrm{O}_{3}(l) + 3\mathrm{Fe}(l)\]

• According to stoichiometry, 3 moles of iron(II) oxide react with 2 moles of aluminum.
• This produces 1 mole of aluminum oxide and 3 moles of iron, illustrating the precise quantitative relationships between reactants and products.

By understanding these relationships, stoichiometry helps us predict the yields of reactions and optimize the use of resources in a chemical process.

Conservation of Mass

The law of conservation of mass is a fundamental principle guiding chemical equations and stoichiometry. It states that in a chemical reaction, mass is neither created nor destroyed. Therefore, the mass of the reactants must equal the mass of the products.
When balancing a chemical equation, ensure that the same number of atoms for each element exists on both sides of the equation. For instance, in Reaction (b):\[\mathrm{MnO}_{2}(l) + 2\mathrm{Al}(l) \rightarrow \mathrm{Al}_{2}\mathrm{O}_{3}(l) + \mathrm{Mn}(l)\]Initially, the unbalanced equation did not satisfy this law. We adjusted coefficients to ensure that the number of each type of atom was equal on both sides of the equation. Once balanced, for every 4 moles of aluminum, there are also 6 oxygen atoms maintained throughout both sides.
This principle emphasizes that we should not lose or gain any atoms in the reactions, facilitating a complete and thorough balancing process.

Chemical Reactions

Chemical reactions describe processes in which substances transform into different substances. The substances we begin with, known as reactants, undergo a transformation to become products.

• A reactant, such as \(\mathrm{FeO}\) in reaction (a), interacts with another chemical, \(\mathrm{Al}\), to produce new substances \(\mathrm{Al}_{2}\mathrm{O}_{3}\) and \(\mathrm{Fe}\).

A chemical equation visually represents this transformation, guiding us to balance it by showing the change clearly.
Classifying reactions can further enhance understanding:- **Synthesis reactions**: Multiple reactants combine to form a single product. - **Decomposition reactions**: A single compound breaks down into multiple products.- **Single replacement reactions**: An element in a compound is replaced by another element.Every balanced equation represents these changes accurately, capturing the essence of chemical reactions and ensuring the conservation of all atoms involved.