How many times must be conentration of substances `B_(2)` in the system `2A_(2)(g)+B_(2)(g)to2A_(2)B(g)` be increased for the rate of the forward reaction to remain unchanged when the concentration of substances `A_(2)` is lowered to one -- fourth of its initial value ?

Explanation

To solve the problem, we need to determine how many times the concentration of substance \( B_2 \) must be increased when the concentration of substance \( A_2 \) is lowered to one-fourth of its initial value, while keeping the rate of the forward reaction unchanged.

### Step-by-Step Solution:

1. **Write the Reaction and Rate Expression**:
The given reaction is:
\[
2A_2(g) + B_2(g) \rightarrow 2AB(g)
...