solve step by step:Incomplete and Unbalanced Half-reaction Equation

HCIO2(aq) → Cl2(g)

This incomplete half-reaction must be completed and balanced for it to represent the half-reaction of chlorous acid in an acidic solution.

6. Which of the following rows identifies the lowest whole number coefficients for H+ (aq) and H2O(I) that are required to complete and balance the half-reaction equation above?

Row

H+(aq)

H2O(1)

8

4

3

2

4

2

6

4

To solve the step-by-step process of completing and balancing the half-reaction equation of chlorous acid (HClO₂) to chlorine gas (Cl₂) in an acidic solution, we need to follow these steps:

### Step 1: Write the incomplete half-reaction
\[ \text{HClO}_2 (aq) \rightarrow \text{Cl}_2 (g) \]

### Step 2: Determine oxidation states
For HClO₂:
- H has an oxidation state of +1.
- O has an oxidation state of -2 (since there are two oxygens, the total for oxygen is -4).
- To balance the overall charge, Cl must have an oxidation state of +3.

For Cl₂:
- Cl₂ is a diatomic molecule where each Cl has an oxidation state of 0.

### Step 3: Identify the change in oxidation state
- Cl changes from +3 in HClO₂ to 0 in Cl₂.

### Step 4: Balance the change in oxidation states
- Each Cl in HClO₂ changes from +3 to 0, so each HClO₂ provides one Cl.
- Since Cl₂ has two Cl atoms, two HClO₂ molecules are needed:
\[ 2\text{HClO}_2 \rightarrow \text{Cl}_2 \]

### Step 5: Balance the oxygen atoms by adding H₂O
- There are 4 oxygen atoms on the left (from 2 HClO₂).
- To balance this, we need 4 H₂O molecules on the right:
\[ 2\text{HClO}_2 \rightarrow \text{Cl}_2 + 4\text{H}_2\text{O} \]

### Step 6: Balance the hydrogen atoms by adding H⁺ ions
- There are 4 H₂O molecules on the right, giving 8 H atoms.
- To balance the 2 HClO₂ molecules (2 H atoms), we need to add 6 H⁺ on the left:
\[ 2\text{HClO}_2 + 6\text{H}^+ \rightarrow \text{Cl}_2 + 4\text{H}_2\text{O} \]

### Step 7: Verify the charge balance
- On the left: There are 6 positive charges from H⁺.
- On the right: There are no charges.

The final balanced half-reaction is:
\[ 2\text{HClO}_2 + 6\text{H}^+ \rightarrow \text{Cl}_2 + 4\text{H}_2\text{O} \]

### Step 8: Identify the coefficients for H⁺ and H₂O
From the balanced half-reaction:
- Coefficient for H⁺ is 6.
- Coefficient for H₂O is 4.

### Answer
The correct row identifying the lowest whole number coefficients for H⁺ and H₂O is:

**Row 6: 4**

**Coefficients:**

- \( \text{H}^+ = 6 \)
- \( \text{H}_2\text{O} = 4 \)

### Conclusion
The lowest whole number coefficients for \( \text{H}^+ \) and \( \text{H}_2\text{O} \) required to complete and balance the half-reaction equation are 6 and 4, respectively.

Do you want any further details or have any questions?

Here are five questions you might ask:
1. How do you balance redox reactions in basic solutions?
2. Can you explain the method of balancing equations using the oxidation number method?
3. What are common mistakes to avoid while balancing chemical equations?
4. How do you determine the oxidation state of an element in a compound?
5. Can you explain how to balance complex ionic equations?

**Tip:** When balancing redox reactions, it's crucial to balance the atoms and charges separately to ensure the equation is fully balanced.

Learn how to complete and balance the half-reaction equation of chlorous acid (HClO₂) to chlorine gas (Cl₂) in an acidic solution step-by-step. This problem involves chemical reactions, redox reactions, and balancing equations. Suitable for advanced high school and beyond.

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