Problem 0 - 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 given equation, \(\mathrm{Fe}(\mathrm{s})+\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s})\), is not balanced because the charges are not equal on both sides (+1 on reactants side and +2 on products side). To balance the equation, the number of Silver ions in the reactants should be doubled: $$\mathrm{Fe}(\mathrm{s})+ 2\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})+ 2\mathrm{Ag}(\mathrm{s})$$

Step 1: Identify the reactants and products

First, let's identify the reactants and products in the given equation: Reactants: Iron (\(\mathrm{Fe}\)) and Silver ions (\(\mathrm{Ag}^+\)) Products: Iron ions (\(\mathrm{Fe}^{2+}\)) and Silver (\(\mathrm{Ag}\))

Step 2: Count the number of atoms for each element

Now, let's count the number of atoms for each element on the reactant and product sides: Reactants: - Iron (\(\mathrm{Fe}\)) atoms: 1 - Silver (\(\mathrm{Ag}\)) atoms: 1 Products: - Iron (\(\mathrm{Fe}\)) atoms: 1 - Silver (\(\mathrm{Ag}\)) atoms: 1

Step 3: Compare the number of atoms on both sides

Since the number of Iron and Silver atoms on the reactant side and the product side are equal (1 atom each), the equation appears to be balanced in terms of the atoms. Reactants: 1 \(\mathrm{Fe}\) atom + 1 \(\mathrm{Ag}\) atom Products: 1 \(\mathrm{Fe}\) atom + 1 \(\mathrm{Ag}\) atom

Step 4: Check the charges on both sides of the equation

Lastly, we need to confirm that the charges on both sides of the equation are equal. Here is the charge distribution: Reactants: - Iron (\(\mathrm{Fe}\)) charge: 0 (neutral) - Silver ion (\(\mathrm{Ag}^+\)) charge: +1 Total charge on reactants side: +1 Products: - Iron ion (\(\mathrm{Fe}^{2+}\)) charge: +2 - Silver (\(\mathrm{Ag}\)) charge: 0 (neutral) Total charge on products side: +2

Step 5: Conclusion

Since the charges on both sides of the equation are not equal (+1 on reactants side and +2 on products side), the given equation is not balanced. To balance the equation, the number of Silver ions in the reactants should be doubled so that the sum of the charges on both sides of the equation becomes equal: $$\mathrm{Fe}(\mathrm{s})+ 2\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})+ 2\mathrm{Ag}(\mathrm{s})$$

Key Concepts

Understanding Reactants and Products

In every chemical reaction, it's essential to first identify what chemicals are reacting and what chemicals are produced. These are known as reactants and products. In the context of our given equation, the reactants are the substances you start with: Iron (\(\mathrm{Fe}\)) and Silver ions (\(\mathrm{Ag}^+\)). The products, on the other hand, are the new substances formed by the reaction: Iron ions (\(\mathrm{Fe}^{2+}\)) and Silver (\(\mathrm{Ag}\)). These terms help us categorize the transformation occurring at an atomic level.
By determining what we have before and after the reaction, we ensure a comprehensive understanding of the substance behavior in the chemical equation. This foundational step is crucial as it sets the stage for further analysis such as counting atoms and balancing charges.

Mastering Atom Counting

Atom counting is a process of tallying the number of atoms of each element present on both sides of a chemical equation. This ensures that mass is conserved, as per the Law of Conservation of Mass. In our example equation, we need to count the \(\mathrm{Fe}\) and \(\mathrm{Ag}\) atoms on both the reactant and product sides.

• The reactant side has 1 Iron (\(\mathrm{Fe}\)) atom and 1 Silver (\(\mathrm{Ag}^+\)) ion.
• The product side has 1 Iron (\(\mathrm{Fe}^{2+}\)) ion and 1 Silver (\(\mathrm{Ag}\)) atom.

Since the number of atoms for each element remains the same (1 \(\mathrm{Fe}\) atom and 1 \(\mathrm{Ag}\) atom on each side), the equation initially seems balanced in terms of atom count. Ensuring atoms are balanced is an important step before addressing any charge imbalances.

Balancing Charges

Charge balance is equally critical in forming a properly balanced chemical equation. Just like atoms, charges must be the same on both sides of the equation. In our equation, we initially observe:

• The reactants have a total charge of +1 (0 from \(\mathrm{Fe}\) and +1 from \(\mathrm{Ag}^+\)).
• The products have a total charge of +2 (+2 from \(\mathrm{Fe}^{2+}\) and 0 from \(\mathrm{Ag}\)).

As a result, the charges do not match, indicating a charge imbalance. To resolve this, we adjust the coefficients of the ions where necessary. By doubling the Silver ions in the reactants, we make both sides electrically neutral overall:\[\mathrm{Fe}(\mathrm{s})+ 2\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})+ 2\mathrm{Ag}(\mathrm{s})\] Through this adjustment, both the number of particles and the charges are balanced, producing a correctly balanced chemical equation.