Question

The equation \(\mathrm{Ag}^{+}(a q)+\mathrm{Cu}(s) \rightarrow \mathrm{Cu}^{2+}(a q)+\mathrm{Ag}(s)\) has equal numbers of each type of element on each side of the equation. This equation, however, is not balanced. Why is this equation not balanced? Balance the equation.

Short answer

The given equation, \( \mathrm{Ag}^{+}(aq) + \mathrm{Cu}(s) \rightarrow \mathrm{Cu}^{2+}(aq) + \mathrm{Ag}(s) \), is not initially balanced because the coefficients for each element are not specified. However, upon inspection, it turns out that each side has one silver (Ag) and one copper (Cu) atom, so applying coefficients of 1 for each molecule balances the equation. The balanced equation is: \( \mathrm{Ag}^{+}(aq) + \mathrm{Cu}(s) \rightarrow \mathrm{Cu}^{2+}(aq) + \mathrm{Ag}(s) \).

Step-by-step solution

Identify the unbalanced elements in the equation

The given equation is: \[ \mathrm{Ag}^{+}(aq) + \mathrm{Cu}(s) \rightarrow \mathrm{Cu}^{2+}(aq) + \mathrm{Ag}(s) \] While it has the same number of types of elements on both sides of the equation, the coefficients for each of these elements are not specified. We will need to determine the appropriate coefficients to ensure the atoms for each element are equal on both sides of the reaction.

Balance each element

Let's balance the individual elements in the equation. 1. First, we will balance the silver (Ag) atoms: \[ \mathrm{Ag}^{+}(aq) + \mathrm{Cu}(s) \rightarrow \mathrm{Cu}^{2+}(aq) + \mathrm{Ag}(s) \] The silver atoms are already balanced on both sides, with one Ag on each side. 2. Now, we will balance the copper (Cu) atoms: \[ \mathrm{Ag}^{+}(aq) + \mathrm{Cu}(s) \rightarrow \mathrm{Cu}^{2+}(aq) + \mathrm{Ag}(s) \] The copper atoms are also balanced on each side, with one Cu on each side. By applying coefficients of 1 for each molecule, the equation is now balanced. Therefore, the balanced equation is:

Write the balanced equation

The balanced equation is: \[ \mathrm{Ag}^{+}(aq) + \mathrm{Cu}(s) \rightarrow \mathrm{Cu}^{2+}(aq) + \mathrm{Ag}(s) \]

Key concepts

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are processes that involve the transfer of electrons between chemicals. These reactions are fundamental to many natural and industrial processes. In a redox reaction, oxidation and reduction occur simultaneously:

• Oxidation is the process where a chemical species loses electrons.
• Reduction is the process where a chemical species gains electrons.

In the provided exercise, silver ions (\(\mathrm{Ag}^{+}\)) gain an electron to form silver metal (\(\mathrm{Ag}(s)\)), while copper metal (\(\mathrm{Cu}(s)\)) loses two electrons to form copper ions (\(\mathrm{Cu}^{2+}\)). Hence, copper is oxidized, and silver is reduced. Recognizing these processes helps in understanding how substances change during reactions. These insights are key for solving redox equations and making sure reactions are balanced.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is crucial for determining the correct amounts, or proportions, of substances reacting with each other.

• In a balanced chemical equation, the quantities of all reactants and products are matched to conserve mass.
• This means, the number of atoms for each element is the same on both sides of the equation.

In the original exercise, stoichiometry tells us that even though the labels are correct, balancing involves ensuring not just the elements, but also their ionic charges or states. Therefore, while the reaction initially had equal types of elements on both sides, proper stoichiometric balancing also requires considering the electrical neutrality and charge balance in the equation.

Oxidation and Reduction

Understanding oxidation and reduction is crucial to correctly balancing redox reactions. Remember:

• Oxidation involves the loss of electrons (\(\mathrm{Cu} \rightarrow \mathrm{Cu}^{2+} + 2e^-\)).
• Reduction involves the gain of electrons (\(\mathrm{Ag}^{+} + e^- \rightarrow \mathrm{Ag}\)).

In balancing redox equations, identify which atoms undergo oxidation and reduction by analyzing changes in their oxidation states. Connect the dots by ensuring that the number of electrons lost in oxidation equals the number gained in reduction, maintaining electric charge balance. Oxidation numbers are invaluable tools in gauging the number of electrons exchanged and finding errors in otherwise seemingly balanced equations. It’s about balancing more than just atoms—charges must be balanced too!