6 mole of `FeC_2 O_4` on treatment with 2 mole of `K_2 Cr_2 O_7` in acidic medium evolves x litre of `CO_2` gas at STP. The value of x would be:

Options

A. `22.4 I`
B. `44.8 I`
C. `67.2 I`
D. `179.2 I`

Answer

To solve the problem, we need to determine how many liters of CO₂ gas are evolved when 6 moles of FeC₂O₄ react with 2 moles of K₂Cr₂O₇ in an acidic medium.

### Step-by-Step Solution:

1. **Write the Balanced Chemical Equation:**
The balanced equation for the reaction is:
\[ K_2Cr_2O_7 + 7FeC_2O_4 + 14H^+ \rightarrow 2Cr^{3+} + 7Fe^{2+} + 2K^+ + 7H_2O + 4CO_2 \]
This shows that 1 mole of K₂Cr₂O₇ reacts with 7 moles of FeC₂O₄ to produce 4 moles of CO₂.

2. **Determine the Stoichiometric Ratios:**
From the balanced equation, we see that:
- 1 mole of K₂Cr₂O₇ produces 4 moles of CO₂.
- 7 moles of FeC₂O₄ are needed for 1 mole of K₂Cr₂O₇.

3. **Identify the Limiting Reagent:**
We have 6 moles of FeC₂O₄ and 2 moles of K₂Cr₂O₇.
- To react with 6 moles of FeC₂O₄, we need:
\[ \frac{6 \text{ moles FeC}_2\text{O}_4}{7} = \frac{6}{7} \text{ moles of K}_2\text{Cr}_2\text{O}_7 \approx 0.857 \text{ moles} \]
- Since we have 2 moles of K₂Cr₂O₇ available, which is more than needed, FeC₂O₄ is not the limiting reagent.
- However, we can also calculate how much FeC₂O₄ is required for 2 moles of K₂Cr₂O₇:
\[ 2 \text{ moles of K}_2\text{Cr}_2\text{O}_7 \times 7 \text{ moles of FeC}_2\text{O}_4 = 14 \text{ moles of FeC}_2\text{O}_4 \]
- Since we only have 6 moles of FeC₂O₄, K₂Cr₂O₇ is the limiting reagent.

4. **Calculate the Moles of CO₂ Produced:**
From the stoichiometry of the reaction:
- 1 mole of K₂Cr₂O₇ produces 4 moles of CO₂.
- Therefore, 2 moles of K₂Cr₂O₇ will produce:
\[ 2 \text{ moles of K}_2\text{Cr}_2\text{O}_7 \times 4 \text{ moles of CO}_2 = 8 \text{ moles of CO}_2 \]

5. **Convert Moles of CO₂ to Volume at STP:**
At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 liters. Thus, the volume of 8 moles of CO₂ is:
\[ 8 \text{ moles of CO}_2 \times 22.4 \text{ L/mole} = 179.2 \text{ liters} \]

### Final Answer:
The value of \( x \) is **179.2 liters**.

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