`underset("Orange")(Cr_(2)O_(7)^(2-)) underset underset(pH=y)(larr)overset(pH=x)to underset("green")(CrO_(4)^(2-))`
The change is based on change in pH, the probable values of x and y can be

Options

A. `8,6`
B. `8,10`
C. `4,6`
D. change is independent of pH

Answer

To solve the problem regarding the change of dichromate ion (\(Cr_2O_7^{2-}\)) to chromate ion (\(CrO_4^{2-}\)) based on pH, we need to analyze the conditions under which this transformation occurs.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- The dichromate ion (\(Cr_2O_7^{2-}\)) is orange in color, while the chromate ion (\(CrO_4^{2-}\)) is green in color.
- The transformation from dichromate to chromate involves a change in the oxidation state of chromium from +6 in chromate to +7 in dichromate.

2. **Identifying the pH Conditions**:
- The conversion of dichromate ion to chromate ion occurs in an acidic medium. This means that the pH at which this conversion happens (let's call it \(x\)) must be less than 7.
- Conversely, the conversion from chromate ion back to dichromate ion occurs in a basic medium, which means the pH (let's call it \(y\)) must be greater than 7.

3. **Setting the Conditions for \(x\) and \(y\)**:
- From the analysis, we can conclude:
- \(x < 7\) (for the conversion from dichromate to chromate)
- \(y > 7\) (for the conversion from chromate to dichromate)

4. **Evaluating the Options**:
- We need to evaluate the given options to find pairs of \(x\) and \(y\) that satisfy these conditions.
- Any option where \(x\) is greater than or equal to 7 or \(y\) is less than or equal to 7 will be incorrect.

5. **Conclusion**:
- The correct values for \(x\) and \(y\) must satisfy:
- \(x < 7\)
- \(y > 7\)

### Final Answer:
The probable values of \(x\) and \(y\) are such that \(x < 7\) and \(y > 7\).

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