3 moles of A and 4 moles of B are mixed together and allowed to come into equilibrium according to the following reaction
`A(g) + 4 B(g) hArr 2 C (g) + 3 D (g)`
When equilirium is reached , there is 1 mole of C. The equilibrium extent of the reaction is

Options

A. `1//4`
B. `1//3`
C. `1//2`
D. 1

Explanation

To solve the problem, we need to determine the extent of the reaction (α) based on the given equilibrium conditions. Let's break it down step by step.

### Step 1: Write the balanced chemical equation
The reaction is given as:
\[ A(g) + 4B(g) \rightleftharpoons 2C(g) + 3D(g) \]

### Step 2: Identify initial moles of reactants
From the problem, we know:
- Initial moles of A = 3 moles
- Initial moles of B = 4 moles

### Step 3: Set up the change in moles at equilibrium
Let the extent of the reaction be represented by \( \alpha \). The changes in moles of each species at equilibrium can be expressed as follows:
- Moles of A at equilibrium = \( 3 - \alpha \)
- Moles of B at equilibrium = \( 4 - 4\alpha \)
- Moles of C at equilibrium = \( 2\alpha \)
- Moles of D at equilibrium = \( 3\alpha \)

### Step 4: Use the information given about C
We know that at equilibrium, there is 1 mole of C:
\[ 2\alpha = 1 \]

### Step 5: Solve for α
From the equation \( 2\alpha = 1 \):
\[ \alpha = \frac{1}{2} \]

### Step 6: Conclusion
The equilibrium extent of the reaction is \( \alpha = \frac{1}{2} \).

### Summary of the solution:
The equilibrium extent of the reaction is \( \frac{1}{2} \).

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