`Cr_(2)O_(7)^(2-)overset([H^(+)])rarrCrO_(4)^(-2)overset((H^(+))rarrCr_(2)O_(7)^(2-)`
Values of `(H^(+))` would be respectively :-

Options

A. `10^(-4) & 10^(-5)`
B. `10^(-4),10^(-8)`
C. `10^(-8), 10^(-4)`
D. `10^(8),10^(-9)`

Answer

To solve the problem, we need to analyze the two reactions involving the dichromate ion (Cr₂O₇²⁻) and the chromate ion (CrO₄²⁻) in terms of their oxidation states and the conditions (pH) under which these reactions occur.

### Step-by-Step Solution:

1. **Identify the Reactions:**
- The first reaction is the conversion of dichromate ion (Cr₂O₇²⁻) to chromate ion (CrO₄²⁻).
- The second reaction is the conversion of chromate ion (CrO₄²⁻) back to dichromate ion (Cr₂O₇²⁻).

2. **Determine the Oxidation States:**
- In Cr₂O₇²⁻, the oxidation state of chromium (Cr) can be calculated as follows:
\[ 2x + 7(-2) = -2 \implies 2x - 14 = -2 \implies 2x = 12 \implies x = +6 \]
- Thus, the oxidation state of Cr in Cr₂O₇²⁻ is +6.
- In CrO₄²⁻, the oxidation state of chromium is:
\[ x + 4(-2) = -2 \implies x - 8 = -2 \implies x = +6 \]
- The oxidation state remains +6 for Cr in CrO₄²⁻ as well.

3. **Analyze the First Reaction (Dichromate to Chromate):**
- The conversion from Cr₂O₇²⁻ to CrO₄²⁻ occurs under basic conditions (high pH).
- This means that the concentration of H⁺ ions (denoted as x) must be low, specifically:
\[ [H^+] < 10^{-7} \text{ M} \quad \text{(pH > 7)} \]

4. **Analyze the Second Reaction (Chromate to Dichromate):**
- The conversion from CrO₄²⁻ to Cr₂O₇²⁻ occurs under acidic conditions (low pH).
- This means that the concentration of H⁺ ions (denoted as y) must be high, specifically:
\[ [H^+] > 10^{-7} \text{ M} \quad \text{(pH < 7)} \]

5. **Conclusion:**
- From the analysis, we conclude:
- For the first reaction (dichromate to chromate), x must be less than \(10^{-7}\) M.
- For the second reaction (chromate to dichromate), y must be greater than \(10^{-7}\) M.

6. **Choose the Correct Values:**
- The suitable option for x and y that satisfies these conditions is:
- \(x = 10^{-8}\) (which is less than \(10^{-7}\))
- \(y = 10^{-4}\) (which is greater than \(10^{-7}\))

### Final Answer:
The values of \(H^+\) would be respectively: \(10^{-8}\) and \(10^{-4}\).