`4` mol of carbon dioxide was heated in `1 dm^(3)` vessel under conditions which produced at equilibrium `25%` dissociation into carbon monoxide and oxygen. The number of moles of carbon monoxide produced

Options

A. `0.5`
B. `1.0`
C. `2.0`
D. `4.0`

Explanation

To solve the problem, we need to determine the number of moles of carbon monoxide (CO) produced when 4 moles of carbon dioxide (CO2) dissociate by 25% in a 1 dm³ vessel.

### Step-by-Step Solution:

1. **Write the Reaction**:
The dissociation of carbon dioxide can be represented by the following chemical equation:
\[ 2 \text{CO}_2(g) \rightleftharpoons 2 \text{CO}(g) + \text{O}_2(g) \]

2. **Initial Moles**:
Initially, we have 4 moles of CO2. Therefore, we can write:
\[ \text{Initial moles of CO}_2 = 4 \]
\[ \text{Initial moles of CO} = 0 \]
\[ \text{Initial moles of O}_2 = 0 \]

3. **Degree of Dissociation**:
The problem states that there is a 25% dissociation of CO2. This means that 25% of the initial moles of CO2 will dissociate. We can express this mathematically as:
\[ \alpha = 25\% = \frac{25}{100} = 0.25 \]

4. **Calculate the Moles Dissociated**:
Since we started with 4 moles of CO2, the amount that dissociates can be calculated as:
\[ \text{Moles dissociated} = \alpha \times \text{Initial moles of CO}_2 = 0.25 \times 4 = 1 \text{ mole} \]

5. **Calculate the Moles at Equilibrium**:
After dissociation, we can determine the moles of each substance at equilibrium:
- Moles of CO2 remaining:
\[ \text{Moles of CO}_2 = 4 - 1 = 3 \text{ moles} \]
- Moles of CO produced:
Since 2 moles of CO are produced for every 2 moles of CO2 that dissociate, the moles of CO produced will be equal to the moles of CO2 that dissociated:
\[ \text{Moles of CO} = 1 \text{ mole} \]
- Moles of O2 produced:
From the reaction stoichiometry, for every 2 moles of CO2 that dissociate, 1 mole of O2 is produced. Therefore, the moles of O2 produced will be:
\[ \text{Moles of O}_2 = \frac{1}{2} \text{ moles} = 0.5 \text{ moles} \]

6. **Final Answer**:
The number of moles of carbon monoxide (CO) produced is:
\[ \text{Moles of CO} = 1 \text{ mole} \]

### Conclusion:
The number of moles of carbon monoxide produced is **1 mole**.

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