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 l`
B. `44.8 l`
C. `67.2 l`
D. `179.2 l`

Answer

To solve the problem step by step, we need to analyze the chemical reaction and the stoichiometry involved.

### Step 1: Write the balanced chemical equation
The reaction between potassium dichromate (K₂Cr₂O₇) and iron(II) oxalate (FeC₂O₄) in acidic medium can be represented as follows:

\[ K_2Cr_2O_7 + FeC_2O_4 + H^+ \rightarrow Cr^{3+} + Fe^{2+} + K^+ + H_2O + CO_2 \]

### Step 2: Determine the stoichiometry of the reaction
From the balanced equation, we can see that:
- 1 mole of K₂Cr₂O₇ reacts with 2 moles of FeC₂O₄ to produce 4 moles of CO₂.

### Step 3: Calculate the moles of CO₂ produced
Given that we have 2 moles of K₂Cr₂O₇:
- According to the stoichiometry, 2 moles of K₂Cr₂O₇ will produce:
\[ 2 \text{ moles K}_2Cr_2O_7 \rightarrow 2 \times 4 \text{ moles of CO}_2 = 8 \text{ moles of CO}_2 \]

### Step 4: Calculate the volume of CO₂ at STP
At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 liters. Therefore, the volume of 8 moles of CO₂ can be calculated as:
\[ \text{Volume of CO}_2 = 8 \text{ moles} \times 22.4 \text{ L/mole} = 179.2 \text{ L} \]

### Conclusion
Thus, the value of \( x \) (the volume of CO₂ evolved) is:
\[ x = 179.2 \text{ liters} \]

### Final Answer
The value of \( x \) would be **179.2 liters**.

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