Mass action rato or reaction quotient Q for a reaction can be calculate using the law of masss action
`A(g)+B(g) hArr C(g)+D(g)`
`Q=([C][D])/([A][B])`
The value of Q decides whether the reaction is at equilibrium or not.
At equilibrium, `Q=K`
For an equilibrium process, `Q ne K`
when `Q gt K`, reaction will favour backward direction and when `Q lt K`, it will favour direction.
Answer the following questions:
For the reaction:
`2A+B hArr 3C` at `298 K, K_(c)=40`
A `4L` vessel contains `2, 1,` and `4` mol of A, B and c, respectively. The reaction at the same temperature

Options

A. Must proceed in forward direction
B. Must proceed in backward direction
C. Must be in equilibrium
D. Cannot be predicted

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Write the balanced chemical equation and identify the equilibrium constant expression.
The given reaction is:
\[ 2A + B \rightleftharpoons 3C \]

The equilibrium constant expression \( K_c \) for this reaction is given by:
\[ K_c = \frac{[C]^3}{[A]^2[B]} \]

### Step 2: Calculate the concentrations of the reactants and products.
We are given the number of moles of A, B, and C in a 4 L vessel:
- Moles of A = 2
- Moles of B = 1
- Moles of C = 4

To find the concentrations, we use the formula:
\[ \text{Concentration} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]

Calculating the concentrations:
- Concentration of A:
\[ [A] = \frac{2 \text{ moles}}{4 \text{ L}} = 0.5 \, \text{M} \]

- Concentration of B:
\[ [B] = \frac{1 \text{ mole}}{4 \text{ L}} = 0.25 \, \text{M} \]

- Concentration of C:
\[ [C] = \frac{4 \text{ moles}}{4 \text{ L}} = 1 \, \text{M} \]

### Step 3: Calculate the reaction quotient \( Q \).
Using the concentrations calculated, we can now find \( Q \):
\[ Q = \frac{[C]^3}{[A]^2[B]} \]

Substituting the values:
\[ Q = \frac{(1)^3}{(0.5)^2(0.25)} \]

Calculating:
\[ Q = \frac{1}{0.25 \times 0.25} = \frac{1}{0.0625} = 16 \]

### Step 4: Compare \( Q \) with \( K_c \).
Given that \( K_c = 40 \):
- Since \( Q = 16 \) and \( K_c = 40 \), we have:
\[ Q < K_c \]

### Step 5: Determine the direction of the reaction.
Since \( Q < K_c \), the reaction will favor the forward direction to reach equilibrium.

### Final Conclusion:
The reaction will proceed in the forward direction because the reaction quotient \( Q \) is less than the equilibrium constant \( K_c \).

---