**Explanation:**

Given:

- Initial concentration of A, B, C, and D = 1.5 M
- Volume of the vessel = 500 ml

We need to calculate the equilibrium constant (Kc) after 0.5 M of C and D are expelled out.

**Step 1: Write the balanced chemical equation**

Let's assume the balanced chemical equation for the reaction involving A, B, C, and D is:

aA + bB ⇌ cC + dD

**Step 2: Calculate the initial moles of A, B, C, and D**

To calculate the initial moles, we can use the formula:

moles = concentration * volume

Given that the volume is 500 ml and the concentration of A, B, C, and D is 1.5 M, we can calculate the initial moles:

moles of A = 1.5 M * 0.5 L = 0.75
moles of B = 1.5 M * 0.5 L = 0.75
moles of C = 1.5 M * 0.5 L = 0.75
moles of D = 1.5 M * 0.5 L = 0.75

**Step 3: Calculate the change in moles of C and D**

Since 0.5 M of C and D are expelled out, the change in moles can be calculated as:

change in moles of C = initial moles of C - expelled moles of C = 0.75 - (0.5 M * 0.5 L) = 0.75 - 0.25 = 0.5
change in moles of D = initial moles of D - expelled moles of D = 0.75 - (0.5 M * 0.5 L) = 0.75 - 0.25 = 0.5

**Step 4: Calculate the equilibrium moles of C and D**

The equilibrium moles can be calculated as:

equilibrium moles of C = initial moles of C - change in moles of C = 0.75 - 0.5 = 0.25
equilibrium moles of D = initial moles of D - change in moles of D = 0.75 - 0.5 = 0.25

**Step 5: Calculate the equilibrium concentration of C and D**

The equilibrium concentration can be calculated using the formula:

concentration = moles / volume

equilibrium concentration of C = 0.25 moles / 0.5 L = 0.5 M
equilibrium concentration of D = 0.25 moles / 0.5 L = 0.5 M

**Step 6: Calculate the equilibrium constant (Kc)**

The equilibrium constant (Kc) can be calculated using the formula:

Kc = ([C]^c * [D]^d) / ([A]^a * [B]^b)

Given that [C] = [D] = 0.5 M, [A] = [B] = 1.5 M, and a = b = c = d = 1, we can substitute the values and calculate Kc:

Kc = (0.5 *