`CrO_(4)^(2-)`(yellow) changes to `Cr_(2)O_(7)^(2-)`(orange) in pH=x and vice-versa in pH=y. Hence, x and y are:

Options

A. `6, 8`
B. `6, 5`
C. `8, 6`
D. `7, 7`

Explanation

To solve the problem of determining the pH values (x and y) at which the chromate ion \((CrO_4^{2-})\) changes to the dichromate ion \((Cr_2O_7^{2-})\) and vice versa, we can follow these steps:

### Step 1: Understand the Chemical Species
- The chromate ion \((CrO_4^{2-})\) is yellow in color.
- The dichromate ion \((Cr_2O_7^{2-})\) is orange in color.

### Step 2: Identify the pH Conditions
- The conversion of chromate to dichromate occurs in acidic conditions (pH < 7).
- The conversion of dichromate back to chromate occurs in basic conditions (pH > 7).

### Step 3: Establish the pH Values
- Let \(x\) be the pH at which chromate changes to dichromate. Since this reaction occurs in acidic conditions, \(x\) must be less than 7.
- Let \(y\) be the pH at which dichromate changes back to chromate. Since this reaction occurs in basic conditions, \(y\) must be greater than 7.

### Step 4: Analyze the Given Options
- The problem provides several pairs of pH values: (6, 8), (6, 5), (8, 6), and (7, 7).
- Since \(x\) must be less than 7 and \(y\) must be greater than 7, we can eliminate options that do not satisfy these conditions.

### Step 5: Select the Appropriate Pair
- From the options:
- (6, 8): \(x = 6\) (valid, since it's less than 7) and \(y = 8\) (valid, since it's greater than 7).
- (6, 5): \(y = 5\) (invalid, since it's not greater than 7).
- (8, 6): \(x = 8\) (invalid, since it's not less than 7).
- (7, 7): both values are invalid.

Thus, the only valid pair is (6, 8).

### Conclusion
The values of \(x\) and \(y\) are:
- \(x = 6\)
- \(y = 8\)