500 ml vessel contains 1.5 M each of A, B, C and D at equlibrium. If 0.5 M each of C and D are taken out, the value of `K_(c)` for `A+BhArrC+D` will be

Options

A. `1.0`
B. `1/9`
C. `4/9`
D. `8/9`

Answer

To solve the problem step by step, we need to analyze the equilibrium reaction and the changes in concentrations after removing some of the products.

### Step 1: Write the equilibrium expression
The equilibrium reaction is given as:
\[ A + B \rightleftharpoons C + D \]

The equilibrium constant \( K_c \) for this reaction is defined as:
\[ K_c = \frac{[C][D]}{[A][B]} \]

### Step 2: Determine initial concentrations
According to the problem, initially, the concentrations of A, B, C, and D are all 1.5 M in a 500 ml vessel. Therefore:
\[ [A] = 1.5 \, \text{M} \]
\[ [B] = 1.5 \, \text{M} \]
\[ [C] = 1.5 \, \text{M} \]
\[ [D] = 1.5 \, \text{M} \]

### Step 3: Calculate initial \( K_c \)
Substituting the initial concentrations into the equilibrium expression:
\[ K_c = \frac{(1.5)(1.5)}{(1.5)(1.5)} = \frac{2.25}{2.25} = 1 \]

### Step 4: Adjust concentrations after removing C and D
Now, we remove 0.5 M each of C and D. The new concentrations will be:
\[ [C] = 1.5 - 0.5 = 1.0 \, \text{M} \]
\[ [D] = 1.5 - 0.5 = 1.0 \, \text{M} \]
Since we are removing products, the concentrations of A and B will also change as the reaction shifts to re-establish equilibrium. However, we need to determine the new concentrations of A and B.

### Step 5: Determine new concentrations of A and B
According to Le Chatelier's principle, if we decrease the concentration of products (C and D), the equilibrium will shift to the right to produce more products. Thus, the concentrations of A and B will also decrease by the same amount (0.5 M) to maintain equilibrium:
\[ [A] = 1.5 - 0.5 = 1.0 \, \text{M} \]
\[ [B] = 1.5 - 0.5 = 1.0 \, \text{M} \]

### Step 6: Calculate new \( K_c \)
Now we can calculate the new \( K_c \) using the adjusted concentrations:
\[ K_c = \frac{[C][D]}{[A][B]} = \frac{(1.0)(1.0)}{(1.0)(1.0)} = \frac{1.0}{1.0} = 1 \]

### Final Answer
Thus, the value of \( K_c \) for the reaction \( A + B \rightleftharpoons C + D \) after removing 0.5 M each of C and D is:
\[ K_c = 1 \]