A chemical reaction occurs in acid medium while balancing the ionic equation for such reactions to balance hydrogen atoms, we add the following to the side deficient in hydrogen.

\(H^+\)

The correct answer is option 3. \(H^+\).

Let us delve into the process of balancing a chemical reaction in acidic medium, focusing specifically on how hydrogen atoms are balanced and why \( H^+ \) ions are added.

Balancing Chemical Reactions in Acidic Medium

When balancing a redox (oxidation-reduction) chemical equation in acidic medium, several steps are involved:

Write the Unbalanced Equation

Start with writing the unbalanced chemical equation for the reaction. For example:

\(\text{Fe}^{2+} + \text{MnO}_4^- \rightarrow \text{Fe}^{3+} + \text{Mn}^{2+} \)

Balance Oxygen Atoms with \( H_2O \)

Add \( H_2O \) molecules to balance oxygen atoms on both sides of the equation:

\(\text{Fe}^{2+} + \text{MnO}_4^- \rightarrow \text{Fe}^{3+} + \text{Mn}^{2+} + 4H_2O \)

Balance Hydrogen Atoms with \( H^+ \) Ions

Next, balance hydrogen atoms (H) by adding \( H^+ \) ions to the side of the equation that is deficient in hydrogen:

\(\text{Fe}^{2+} + \text{MnO}_4^- + 8H^+ \rightarrow \text{Fe}^{3+} + \text{Mn}^{2+} + 4H_2O\)

Reasoning: In acidic medium, \( H^+ \) ions are present in solution due to the dissociation of acids (such as \( HCl \), \( HNO_3 \), etc.). These \( H^+ \) ions are crucial for balancing the equation because they directly contribute to the number of hydrogen atoms on the respective sides of the equation.

Balance Charge with Electrons \( (e^-) \)

After balancing hydrogen atoms, balance the charge by adding electrons \( (e^-) \) to the side of the equation that has a higher positive charge, or to the side where reduction occurs.

Verify and Adjust

After completing the above steps, verify that the number of atoms of each element and the total charge are balanced on both sides of the equation. Adjust coefficients as necessary to achieve balance.

Answering the Question

Regarding the question about what is added to balance hydrogen atoms in acidic medium:

Options Analysis:

\( H_2O \) (option 1) and \( OH^- \) (option 2) are not typically added directly to balance hydrogen atoms in an acidic medium.

\( H^+ \) ions (option 3) are added because they are readily available in the acidic solution and directly contribute to balancing hydrogen atoms.

Therefore, the correct answer is option (3) \( H^+ \).

In summary, when balancing a chemical reaction in acidic medium, \( H^+ \) ions are added to the side of the equation that lacks sufficient hydrogen atoms. This addition helps balance hydrogen atoms by combining with \( OH^- \) ions (if present) to form \( H_2O \), thereby ensuring the conservation of mass and charge in the balanced equation. Thus, the answer to the question is: (3) \( H^+ \)