`CrO_(4)^(2-)underset(pH=Y)overset(pH=X)(hArr)Cr_(2)O_(7)^(-2)` The pH values of (X) and (Y) are respectively

Options

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

Explanation

To solve the problem involving the equilibrium between chromate ions (CrO4^2-) and dichromate ions (Cr2O7^2-) at different pH levels, we can follow these steps:

### Step 1: Understand the Reaction
The reaction between chromate ions and dichromate ions can be represented as follows:
\[ \text{CrO}_4^{2-} \underset{pH=Y}{\rightleftharpoons} \text{Cr}_2\text{O}_7^{2-} \overset{pH=X}{\leftarrow} \]

### Step 2: Identify Oxidation States
- In CrO4^2-, chromium is in the +6 oxidation state.
- In Cr2O7^2-, chromium is in the +7 oxidation state.

### Step 3: Determine the pH Conditions
- The formation of Cr2O7^2- from CrO4^2- occurs under acidic conditions, which means that the pH (denoted as Y) must be less than 7.
- Conversely, the conversion of Cr2O7^2- back to CrO4^2- occurs under basic conditions, which means that the pH (denoted as X) must be greater than 7.

### Step 4: Establish the Relationship Between pH Values
From the above steps, we can conclude:
- \( Y < 7 \) (for CrO4^2- to Cr2O7^2-)
- \( X > 7 \) (for Cr2O7^2- to CrO4^2-)

### Step 5: Analyze Given Options
We need to find the pair of pH values (X and Y) from the options provided:
1. 6 and 8
2. 6 and 5
3. 8 and 6
4. 7 and 7

From our conclusions:
- \( Y \) must be less than 7, so it cannot be 7 or higher.
- \( X \) must be greater than 7, so it cannot be 6 or lower.

### Step 6: Identify the Correct Option
- Option 1: 6 (Y) and 8 (X) - Valid
- Option 2: 6 (Y) and 5 (X) - Invalid (X must be > 7)
- Option 3: 8 (Y) and 6 (X) - Invalid (Y must be < 7)
- Option 4: 7 (Y) and 7 (X) - Invalid (Y must be < 7)

Thus, the correct answer is **Option 1: 6 and 8**.

### Summary
The pH values of (X) and (Y) are respectively:
- \( Y = 6 \) (for CrO4^2-)
- \( X = 8 \) (for Cr2O7^2-)