Which of the following is correctly balanced half reaction -

Options

A. `AsO_(3)^(-2) + H_(2) O rarr AsO_(4)^(_3) + 2H^(+) -2e^(-)`
B. `H_(2)O_(2) + 2e rarr O_(2) + 2H^(+)`
C. `Cr_(2) O_(7)^(-2) + 14H^(+) rarr 2Cr^(+2)+ 7 H_(2)O - 6 e^(-)`
D. `IO_(3)^(-) + 6 H^(+) rarr I_(2) + 3H_(2) O + 5e^(-)`

Explanation

To determine which of the given half-reactions is correctly balanced, we will analyze each option step by step.

### Step 1: Understand the Concepts of Oxidation and Reduction
- **Oxidation** is the loss of electrons, resulting in an increase in oxidation state.
- **Reduction** is the gain of electrons, resulting in a decrease in oxidation state.

### Step 2: Analyze Each Half-Reaction

#### Option 1: \( \text{AsO}_3^{2-} + 2 \text{H}_2\text{O} \rightarrow \text{AsO}_4^{3-} + 2 \text{H}^+ \)
1. Determine the oxidation states:
- For \( \text{AsO}_3^{2-} \): Let oxidation state of As = x.
\[ x + 3(-2) = -2 \implies x - 6 = -2 \implies x = +4 \]
- For \( \text{AsO}_4^{3-} \):
\[ x + 4(-2) = -3 \implies x - 8 = -3 \implies x = +5 \]
2. Change in oxidation state: \( +4 \) to \( +5 \) indicates oxidation (loss of electrons).
3. Electrons should be lost, not gained. Therefore, the electrons should be on the reactant side, indicating this half-reaction is not correctly balanced.

#### Option 2: \( \text{H}_2\text{O}_2 \rightarrow \text{O}_2 + 2 \text{H}^+ + 2 e^- \)
1. Determine the oxidation states:
- In \( \text{H}_2\text{O}_2 \): O is -1.
- In \( \text{O}_2 \): O is 0.
2. Change in oxidation state: \( -1 \) to \( 0 \) indicates oxidation.
3. The reaction shows a loss of electrons (2 electrons), but the sign is incorrect. Therefore, this half-reaction is not correctly balanced.

#### Option 3: \( \text{Cr}_2\text{O}_7^{2-} + 14 \text{H}^+ + 6 e^- \rightarrow 2 \text{Cr}^{3+} + 7 \text{H}_2\text{O} \)
1. Determine the oxidation states:
- For \( \text{Cr}_2\text{O}_7^{2-} \):
\[ 2x + 7(-2) = -2 \implies 2x - 14 = -2 \implies 2x = 12 \implies x = +6 \]
- For \( \text{Cr}^{3+} \): oxidation state is +3.
2. Change in oxidation state: \( +6 \) to \( +3 \) indicates reduction (gain of electrons).
3. The reaction shows a gain of 6 electrons, which is correctly represented. Therefore, this half-reaction is correctly balanced.

#### Option 4: \( \text{IO}_3^{-} + 6 \text{H}^+ + 5 e^- \rightarrow \text{I}^{0} + 3 \text{H}_2\text{O} \)
1. Determine the oxidation states:
- For \( \text{IO}_3^{-} \):
\[ x + 3(-2) = -1 \implies x - 6 = -1 \implies x = +5 \]
- For \( \text{I}^{0} \): oxidation state is 0.
2. Change in oxidation state: \( +5 \) to \( 0 \) indicates reduction (gain of electrons).
3. The reaction shows a gain of 5 electrons, which is correctly represented. However, the overall balancing of atoms should also be checked. The reaction appears to be balanced, but the electrons should be on the reactant side.

### Conclusion
After analyzing all options, **Option 3** is the correctly balanced half-reaction.