consider the reaction `2A_(g) + B_(g) hArr 2C_(g)` for which `K_c = 350`. if 0.001` mole of each of the reactant and product are mix in a 2.0 L flux in the reaction quotient and spontaneous direction of the system will be

Options

A. `Q_c `= 0.002, the equilibrium shifts to the left
B. `Q_c` = 2000, the equilibrium shifts to the left
C. `Q_c` =0.002, the equilibrium shifts to right
D. `Q_c` = 2000, the equilibrium shifts to right

Answer

To solve the problem, we need to determine the reaction quotient \( Q \) for the given reaction and compare it with the equilibrium constant \( K_c \) to find the direction in which the reaction will proceed.

### Step-by-step Solution:

1. **Write the Reaction and Equilibrium Constant:**
The reaction is given as:
\[ 2A_{(g)} + B_{(g)} \rightleftharpoons 2C_{(g)} \]
The equilibrium constant \( K_c \) for this reaction is given as \( K_c = 350 \).

2. **Determine Initial Moles:**
We are given that 0.001 moles of each reactant and product are mixed in a 2.0 L flask. Therefore, the initial moles are:
- Moles of \( A = 0.001 \)
- Moles of \( B = 0.001 \)
- Moles of \( C = 0.001 \)

3. **Calculate Initial Concentrations:**
The concentration of each species can be calculated using the formula:
\[ \text{Concentration} = \frac{\text{Moles}}{\text{Volume (L)}} \]
For 2.0 L:
\[ [A] = \frac{0.001}{2.0} = 0.0005 \, \text{M} \]
\[ [B] = \frac{0.001}{2.0} = 0.0005 \, \text{M} \]
\[ [C] = \frac{0.001}{2.0} = 0.0005 \, \text{M} \]

4. **Write the Expression for Reaction Quotient \( Q \):**
The reaction quotient \( Q \) is calculated using the formula:
\[ Q = \frac{[C]^2}{[A]^2[B]} \]
Substituting the concentrations:
\[ Q = \frac{(0.0005)^2}{(0.0005)^2 \cdot (0.0005)} = \frac{0.00000025}{0.00000025 \cdot 0.0005} \]
Simplifying this:
\[ Q = \frac{0.00000025}{0.000000125} = 2 \]

5. **Compare \( Q \) with \( K_c \):**
Now we compare \( Q \) with \( K_c \):
\[ Q = 2 \quad \text{and} \quad K_c = 350 \]
Since \( Q < K_c \), the reaction will proceed in the forward direction to form more products.

6. **Conclusion:**
The reaction will shift towards the right (favoring the formation of products \( C \)).