Problem 56 - Chemistry Matter and Change

Question

Is the following equation balanced? Explain. $$ \mathrm{Fe}(\mathrm{s})+\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s}) $$

Step-by-Step Solution

Answer

The equation is not balanced due to differences in charge.

Step 1: Identify Reactants and Products

The given equation is: \[ \mathrm{Fe}(\mathrm{s})+\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s}) \] The reactants are: \( \mathrm{Fe}(\mathrm{s}) \) and \( \mathrm{Ag}^{+}(\mathrm{aq}) \). The products are: \( \mathrm{Fe}^{2+}(\mathrm{aq}) \) and \( \mathrm{Ag}(\mathrm{s}) \).

Step 2: Count Atoms for Each Element

Count the number of atoms for each element on both sides of the equation.- Reactants Side: - \( \mathrm{Fe}: 1 \) - \( \mathrm{Ag}^{+}: 1 \)- Products Side: - \( \mathrm{Fe}^{2+}: 1 \) - \( \mathrm{Ag}: 1 \)

Step 3: Check Charges for Balance

Calculate the net charge on each side of the equation to see if they balance.- Reactants Side: - \( \mathrm{Fe}: 0 \) - \( \mathrm{Ag}^{+}: +1 \) - Total Charge: \(+1\)- Products Side: - \( \mathrm{Fe}^{2+}: +2 \) - \( \mathrm{Ag}: 0 \) - Total Charge: \(+2\)

Step 4: Conclusion on Balance

Atoms are balanced (1 Fe and 1 Ag on each side), but the charges are not balanced. The reactants have a total charge of \(+1\) and the products have a total charge of \(+2\). Thus, the equation is not balanced.

Key Concepts

Oxidation-Reduction Reactions

Oxidation-reduction reactions, also known as redox reactions, are a class of reactions involving the transfer of electrons between two substances. In the equation \( \mathrm{Fe} + \mathrm{Ag}^{+} \rightarrow \mathrm{Fe}^{2+} + \mathrm{Ag} \), we can see a clear example of this type of reaction. Here, we look at the substances involved in the transfer of electrons:

• **Oxidation** occurs when a substance loses electrons. In our equation, the iron (Fe) atom is oxidized as it goes from neutral \( \mathrm{Fe} \) to \( \mathrm{Fe}^{2+} \), which means it loses two electrons.
• **Reduction** happens when a substance gains electrons. The silver ion (\( \mathrm{Ag}^{+} \)) is reduced, as it gains an electron to become neutral silver (\( \mathrm{Ag} \)).

The substance that is oxidized is known as the reducing agent, in this case, Fe. The reducing agent donates electrons to another substance. Conversely, the substance that is reduced is the oxidizing agent, here \( \mathrm{Ag}^{+} \), which accepts electrons.Understanding redox reactions is crucial since they are at the core of many vital processes, whether it be in nature, industrial applications, or even within our bodies.

Charge Balance in Reactions

Chemical equations must be balanced not only in terms of atoms but also in terms of charge to represent an accurate chemical reaction. For our given equation, \( \mathrm{Fe} + \mathrm{Ag}^{+} \rightarrow \mathrm{Fe}^{2+} + \mathrm{Ag} \), it is necessary to analyze the charges on both sides to determine if they are balanced.

Analyzing Charge Imbalance

To understand charge balance, we look at the net charges:

• On the reactants side, we have \( \mathrm{Fe}(s) \) with a charge of 0 and \( \mathrm{Ag}^{+}(aq) \) with a charge of +1. Their total charge is +1.
• On the products side, we have \( \mathrm{Fe}^{2+}(aq) \), which bears a charge of +2, and \( \mathrm{Ag}(s) \) with a charge of 0. This results in a total of +2.

The above analysis shows a major charge imbalance because the charges on the reactants side and the products side do not match. The reactants' net charge is +1, while the products' net charge is +2.Charge imbalances must be corrected for a chemical reaction to be fully balanced. This charge discrepancy often denotes errors in the stoichiometric coefficients of the equation, which need to be adjusted to attain charge balance.

Stoichiometry

Stoichiometry refers to the quantitative relationships between reactants and products in a chemical reaction. It's all about balancing equations so that both the mass and charge are conserved.

Role in Balancing Equations

Stoichiometry involves understanding the mole ratios between substances in a reaction. Consider our chemical equation: \( \mathrm{Fe} + \mathrm{Ag}^{+} \rightarrow \mathrm{Fe}^{2+} + \mathrm{Ag} \).

• The goal of stoichiometry is to ensure the number of atoms of each element and the total charge are equal on both sides of the equation.
• This involves assigning appropriate coefficients to the reactants and products so that conservation laws are respected.
• For reactions where net ions are involved, such as this one, stoichiometry can also involve balancing the electrons exchanged in the reaction.

For students learning stoichiometry, it's important to practice identifying these mole ratios. This practice often requires trials and errors while adjusting coefficients.In our case, the original equation has a charge imbalance, indicating that further stoichiometric adjustments are necessary. Mastering stoichiometry enables one to predict the amounts needed and produced in a reaction, making it a vital skill in chemistry.