In the system `A_((s))hArr2B_((g))+3C_((g))`, if the concentration of `C` at equilibrium is increased by a factor of `2`, it will cause the equilibrium concentration of `B` to change to:

Options

A. two times the original value
B. one half of its original value
C. `2sqrt(2) times` its original value
D. `(1)/(2sqrt(2))times` its original value

Explanation

To solve the problem, we will use the principles of chemical equilibrium and Le Chatelier's principle.

### Step-by-Step Solution:

1. **Write the Equilibrium Expression**:
For the reaction \( A_{(s)} \rightleftharpoons 2B_{(g)} + 3C_{(g)} \), the equilibrium constant \( K_c \) can be expressed as:
\[
K_c = \frac{[B]^2[C]^3}{1}
...