Question

Use the oxidation-number method to balance the following ionic redox equations. a. \(A l+I_{2} \rightarrow A l^{3+}+I^{-}\) b. \(M n O_{2}+B r^{-} \rightarrow M n^{2+}+B r_{2}(\text { in acid solution })\)

Short answer

The final balanced equations for the given ionic redox equations are: a. \(Al +I_{2} \rightarrow Al^{3+} + 2I^- + 3e^-\) b. \(2e^- + MnO_2 + 2Br^- \rightarrow Mn^{2+} + Br_2 + 2H^+ + H_2O\)

Step-by-step solution

Assign oxidation numbers

For each element in the given ionic redox equations, we will assign an oxidation number. a. Al: \(0 \rightarrow +3\), I: \(0 \rightarrow -1\). b. Mn: \(+4 \rightarrow +2\), O: \(-2 \rightarrow -2\), Br: \(-1 \rightarrow 0\).

Identify the elements that undergo a change in oxidation number

After assigning oxidation numbers to the elements, we now identify the elements that undergo a change in oxidation number and determine the difference in the oxidation numbers. a. Al: change of \(3\), I: change of \(1\). b. Mn: change of \(2\), Br: change of \(1\).

Balance the number of atoms for elements whose oxidation number is not changing and balance the charges

We will now balance the number of atoms for elements whose oxidation number does not change and the charges in the equations. a. We insert a coefficient of \(2\) in front of I to balance the number of I atoms: \(Al +I_{2} \rightarrow Al^{3+} + 2I^-\) b. The number of O atoms is already balanced and no change is needed. Just add a coefficient of \(2\) in front of the Br atoms to balance the number of Br atoms: \[MnO_2 + 2Br^- \rightarrow Mn^{2+} + Br_2\]

Add electrons to balance oxidation numbers

Now, add electrons to the appropriate side of the equation so as to balance the change in oxidation numbers. a. Add 3 electrons to the right side: \(Al +I_{2} \rightarrow Al^{3+} + 2I^- + 3e^-\) b. Add 2 electrons to the left side: \[2e^- + MnO_2 + 2Br^- \rightarrow Mn^{2+} + Br_2\]

Ensure both half-reactions are balanced

Now it's time to make sure both half-reactions are balanced in terms of atoms and charges. For both equations a and b, the half-reactions are already balanced.

Add \(H^+\) ions and \(H_2O\) molecules to balance the acid solution (only for equation b)

Since equation b is in an acidic solution, we must add \(H^+\) ions and \(H_2O\) molecules to balance the equation. To balance the O atoms, add 2 \(H^+\) ions to the right side and 1 \(H_2O\) molecule to the left side: \[2e^- + MnO_2 + 2Br^- \rightarrow Mn^{2+} + Br_2 + 2H^+ + H_2O\]

Combine the half-reactions

Now we will combine the half-reactions for both equations a and b: a. \(Al +I_{2} \rightarrow Al^{3+} + 2I^- + 3e^-\) b. \[2e^- + MnO_2 + 2Br^- \rightarrow Mn^{2+} + Br_2 + 2H^+ + H_2O\]

Simplify the equation if necessary

For both equations a and b, the resulting equation is already simplified. Final balanced equations: a. \(Al +I_{2} \rightarrow Al^{3+} + 2I^- + 3e^-\) b. \[2e^- + MnO_2 + 2Br^- \rightarrow Mn^{2+} + Br_2 + 2H^+ + H_2O\]

Key concepts

Oxidation Numbers

Understanding oxidation numbers is crucial in identifying redox reactions. They indicate the degree of oxidation or reduction of an atom in a molecule or ion. An element's oxidation number in its elemental state is zero. For example, in the reactions presented, aluminum (Al) has an oxidation number of zero in Al and plus three in Al\(^{3+}\).
To assign oxidation numbers:

• In compounds, the sum of oxidation numbers equals the overall charge.
• Hydrogen is usually +1, and oxygen is typically -2.
• Assign known oxidation states to elements in a formula, balancing the algebraic total to the molecule or ion's charge.

By determining these numbers, we can identify which elements undergo changes, i.e., are oxidized or reduced during the reaction.

Balancing Chemical Equations

Balancing chemical equations is essential to ensure matter conservation in reactions. It's about making sure the number of each type of atom on the reactants side matches the products side based on the law of conservation of mass.
Steps to balance equations:

• Identify elements that change oxidation numbers.
• Adjust coefficients to balance these changes.
• Ensure non-changing atoms' counts are equal on both sides.

For instance, in balancing the Al + I\(_2\) reaction, we placed a coefficient of 2 before I\(^-\) to keep iodine atoms conserved. Always maintain equal atom counts and charges across the equation.

Half-Reactions

Half-reactions split a redox reaction into two processes—oxidation and reduction parts. In the oxidation process, electrons are lost, while in reduction, they are gained.
These steps involve separating the redox reaction into two:

• Oxidation half-reaction: Electron loss, e.g., Al turning into Al\(^{3+}\).
• Reduction half-reaction: Electron gain, such as I\(^{-}\) formation from I\(_2\).

By separately balancing atom and charge counts in these half-reactions, we often add electrons to one side to ensure the atomic and charge balance. Concluding with combining half-reactions, it around returns complete equations showing entire electron flow details.

Acidic Solutions

When balancing redox reactions in acidic solutions, hydronium ions (H\(^+\)) and water molecules (H\(_2\)O) may be added to achieve balance.
Steps include:

• Determine the oxygen and hydrogen discrepancies.
• Add water molecules and H\(^+\) ions to balance oxygen and hydrogen atoms, respectively.

Consider the MnO\(_2\) + Br\(^-\) reaction. It requires adding water to the left and H\(^+\) ions to the right, ensuring complete atom balance. Working in acidic solutions helps stabilize redox reactions involving hydrogen, particularly in redox systems originating from strong acids.