` A + B hArr C + D, K_c = 5` If at some time the concentration of A, B, C and D are 1, 2, 3, 4M, then find out the direction of reaction at this time.

Options

A. Forward
B. Backward
C. At equilibrium
D. Cannot be found

Answer

To determine the direction of the reaction given the equilibrium constant \( K_c \) and the concentrations of the reactants and products, we can follow these steps:

### Step 1: Write the expression for the equilibrium constant \( K_c \)

For the reaction:
\[ A + B \rightleftharpoons C + D \]

The equilibrium constant \( K_c \) is given by the formula:
\[ K_c = \frac{[C][D]}{[A][B]} \]

### Step 2: Substitute the known values into the \( K_c \) expression

Given:
- Concentration of \( A = 1 \, M \)
- Concentration of \( B = 2 \, M \)
- Concentration of \( C = 3 \, M \)
- Concentration of \( D = 4 \, M \)

We can substitute these values into the expression for \( Q_c \) (the reaction quotient):
\[ Q_c = \frac{[C][D]}{[A][B]} = \frac{(3)(4)}{(1)(2)} \]

### Step 3: Calculate \( Q_c \)

Now, we calculate \( Q_c \):
\[ Q_c = \frac{12}{2} = 6 \]

### Step 4: Compare \( Q_c \) with \( K_c \)

We know that:
- \( K_c = 5 \)
- \( Q_c = 6 \)

Now we compare \( Q_c \) with \( K_c \):
- Since \( Q_c (6) > K_c (5) \), the reaction will shift to the left (backward direction) to reach equilibrium.

### Conclusion

The direction of the reaction at this time is backward.

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