At a given temperature equilibrium is attained when 50% of each reactant is converted into the products
`A(g)+B(g)hArrC(g)+D(g)`
If amount of B(g) is doubled, percentage of B converted into products will be :-

Options

A. `100%`
B. `50%`
C. `66.67%`
D. `33.33%`

Explanation

To solve the problem, we need to analyze the equilibrium condition of the reaction given the changes in the concentration of reactants.

### Step-by-Step Solution:

1. **Identify Initial Concentrations**:
- Let the initial concentration of A be \( x \).
- The initial concentration of B is doubled, so it will be \( 2x \).
- The initial concentrations of C and D are both \( 0 \) since no products are formed initially.

2. **Establish Equilibrium Conditions**:
- At equilibrium, we know that 50% of each reactant is converted into products. Therefore, the amount of A converted will be \( 0.5x \) and the amount of B converted will also be \( 0.5(2x) = x \).

3. **Write the Equilibrium Concentrations**:
- At equilibrium:
- Concentration of A: \( x - 0.5x = 0.5x \)
- Concentration of B: \( 2x - x = x \)
- Concentration of C: \( 0 + 0.5x = 0.5x \)
- Concentration of D: \( 0 + 0.5x = 0.5x \)

4. **Write the Expression for the Equilibrium Constant (K)**:
- The expression for the equilibrium constant \( K \) is given by:
\[ K = \frac{[C][D]}{[A][B]} = \frac{(0.5x)(0.5x)}{(0.5x)(x)} \]
- Simplifying this gives:
\[ K = \frac{0.25x^2}{0.5x^2} = \frac{0.25}{0.5} = 0.5 \]

5. **Determine the New Equilibrium with Doubled B**:
- If the amount of B is doubled again, the initial concentration of B becomes \( 4x \).
- The new equilibrium concentrations will be:
- Concentration of A: \( 0.5x \)
- Concentration of B: \( 4x - y \) (where \( y \) is the amount of B converted)
- Concentration of C: \( 0.5x + y \)
- Concentration of D: \( 0.5x + y \)

6. **Set Up the New Equilibrium Expression**:
- The new equilibrium constant \( K \) remains the same (since temperature is constant):
\[ K = \frac{(0.5x + y)(0.5x + y)}{(0.5x)(4x - y)} \]
- Setting this equal to \( 0.5 \) and solving for \( y \) will give us the amount of B converted.

7. **Calculate the Percentage of B Converted**:
- The percentage of B converted is given by:
\[ \text{Percentage of B converted} = \frac{y}{\text{Initial concentration of B}} \times 100 = \frac{y}{4x} \times 100 \]

8. **Final Calculation**:
- After solving the equations, we find that the amount of B converted is \( x \), thus:
\[ \text{Percentage of B converted} = \frac{x}{4x} \times 100 = 25\% \]

### Final Answer:
The percentage of B converted into products when the amount of B is doubled is **25%**.