`Cr_(2)O_(7)^(2-)overset(pH=x)rarrCrO_(4)^(2-)overset(pH=y)rarrCr_(2)O_(7)^(2-)`
x and y can be :

Options

A. 4 and 5
B. 4 and 8
C. 8 and 4
D. 8 and 9

Answer

To solve the question regarding the conversion of dichromate ions (Cr₂O₇²⁻) to chromate ions (CrO₄²⁻) and vice versa, we need to analyze the pH conditions under which these conversions occur.

### Step-by-Step Solution:

1. **Understanding the Species Involved**:
- We have two species: dichromate ion (Cr₂O₇²⁻) and chromate ion (CrO₄²⁻).
- The conversion from Cr₂O₇²⁻ to CrO₄²⁻ occurs in a basic medium, while the reverse conversion occurs in an acidic medium.

2. **Conversion from Dichromate to Chromate**:
- The reaction can be represented as:
\[ \text{Cr}_2\text{O}_7^{2-} + 2 \text{OH}^- \rightarrow 2 \text{CrO}_4^{2-} + \text{H}_2\text{O} \]
- This reaction requires the addition of a base (alkali), which increases the pH of the solution.
- Therefore, for this conversion, the pH (denoted as x) must be greater than 7:
\[ x > 7 \]

3. **Conversion from Chromate to Dichromate**:
- The reaction can be represented as:
\[ \text{CrO}_4^{2-} + 2 \text{H}^+ \rightarrow \text{Cr}_2\text{O}_7^{2-} + \text{H}_2\text{O} \]
- This reaction requires the addition of an acid, which decreases the pH of the solution.
- Therefore, for this conversion, the pH (denoted as y) must be less than 7:
\[ y < 7 \]

4. **Conclusion**:
- From the analysis, we conclude that:
- \( x > 7 \) (for the conversion from Cr₂O₇²⁻ to CrO₄²⁻)
- \( y < 7 \) (for the conversion from CrO₄²⁻ to Cr₂O₇²⁻)

### Final Answer:
The values of x and y can be summarized as:
- \( x > 7 \)
- \( y < 7 \)