A' reacts by following two parallel reactions to give B& C If half of 'A' goes into reaction I and other half goes to reaction-II . Then , select the correct statement(s)
`A+N overset(I) to B +L`
`A+N overset(II)to (1)/(2) B+(1)/(2)(C)+L`

Options

A. B will be always greater than C
B. If 2 mole of C are formed then total 2 mole of B are also formed
C. If 2 mole of C are formed then total 4 mole of B are also formed
D. If 2 mole of C are formed then total 6 mole of B are also formed

Answer

To solve the problem, we need to analyze the two parallel reactions involving the substance A. Let's break down the steps systematically.

### Step 1: Write the Reactions
We have two reactions:
1. Reaction I: \( A + N \rightarrow B + L \)
2. Reaction II: \( A + N \rightarrow \frac{1}{2}B + \frac{1}{2}C + L \)

### Step 2: Define the Amount of A
Let’s assume we start with \( x \) moles of A. According to the problem, half of A goes into each reaction:
- Amount of A in Reaction I: \( \frac{x}{2} \)
- Amount of A in Reaction II: \( \frac{x}{2} \)

### Step 3: Determine the Products from Each Reaction
Now, we will calculate the amount of B and C produced from each reaction:
- From Reaction I:
- Since \( \frac{x}{2} \) moles of A react, the amount of B produced will be \( \frac{x}{2} \) moles (assuming a 1:1 stoichiometry).

- From Reaction II:
- Since \( \frac{x}{2} \) moles of A react, the amount of B produced will be \( \frac{1}{4}x \) moles (because only half of B is produced).
- The amount of C produced will be \( \frac{1}{4}x \) moles (because only half of C is produced).

### Step 4: Total Moles of B and C
Now, we can calculate the total moles of B and C produced:
- Total moles of B:
\[ B_{total} = B_{I} + B_{II} = \frac{x}{2} + \frac{1}{4}x = \frac{2}{4}x + \frac{1}{4}x = \frac{3}{4}x \]

- Total moles of C:
\[ C_{total} = C_{II} = \frac{1}{4}x \]

### Step 5: Compare the Amounts of B and C
Now we can compare the total moles of B and C:
- Since \( \frac{3}{4}x > \frac{1}{4}x \), it is clear that the total moles of B are always greater than the total moles of C.

### Step 6: Analyze the Given Statements
1. **Statement 1**: B is always greater than C. This is **correct**.
2. **Statement 2**: If 2 moles of C are formed, then total moles of B are...
- If \( C = 2 \) moles, then:
\[ \frac{1}{4}x = 2 \implies x = 8 \]
- Therefore, total moles of B:
\[ B_{total} = \frac{3}{4}x = \frac{3}{4} \times 8 = 6 \text{ moles} \]
- This statement is also **correct**.

### Conclusion
The correct statements are:
- B is always greater than C.
- If 2 moles of C are formed, then total moles of B are 6.