5.6 x 10-6 mol of A and 5 x 10-5 mol of B are mixed in a 200 mL flask. The system is represented by the equation:

2A(G) + B(G) <--> 3C(G)

At equilibrium, there is 4.8 x 10-5 mol of B. Calculate the value of the equilibrium constant.

(A) = 5.6E-6/0.2 = 2.8E-5M

(B) = 5E-5/0.2 = 2.5E-4M

.........2A + B ==> 3C
I.....2.8E-5..2.5E-4..0
C.......-2x...-x....3x
E...2.8E-5-2x..2.5E-4-x...3x

We know B at equilibrium = 4.8E-5 mol/0.2L = 2.4E-4; therefore,
2.5E-4-x = 2.4E-4
Solve for x which lets you work out A and C at equilibrium. Then substitute into Keq expression and solve for K.

To calculate the equilibrium constant, you need to use the equilibrium concentrations of A, B, and C.

Here's how you can find the equilibrium concentrations:

1. Firstly, let's determine the change in the number of moles for A and B. Since the balanced equation shows that 2 moles of A react with 1 mole of B to form 3 moles of C, the change in moles of A and B will be:

Change in moles of A = initial moles of A - moles of C
= 5.6 x 10^(-6) mol - (3/2) × change in moles of C

Change in moles of B = initial moles of B - moles of C
= 5 x 10^(-5) mol - change in moles of C

2. Since we know that at equilibrium, there is 4.8 x 10^(-5) mol of B, we can substitute this value into the equation and solve for the change in moles of C:

Change in moles of B = 5 x 10^(-5) mol - change in moles of C
4.8 x 10^(-5) mol = 5 x 10^(-5) mol - change in moles of C
change in moles of C = 5 x 10^(-5) mol - 4.8 x 10^(-5) mol
change in moles of C = 0.2 x 10^(-5) mol

3. Now that we know the change in moles of C, we can substitute this value back into the equations to find the change in moles of A and B:

Change in moles of A = 5.6 x 10^(-6) mol - (3/2) × (0.2 x 10^(-5) mol)
Change in moles of B = 5 x 10^(-5) mol - 0.2 x 10^(-5) mol

4. Finally, you can find the equilibrium concentrations of A, B, and C by adding the change in moles to their respective initial moles:

Equilibrium moles of A = initial moles of A + change in moles of A
Equilibrium moles of B = initial moles of B + change in moles of B
Equilibrium moles of C = change in moles of C

5. Once you have the equilibrium moles of A, B, and C, divide each of them by the volume of the flask (200 mL) to get their respective concentrations.

6. Now, substitute these equilibrium concentrations into the equilibrium constant expression:

Equilibrium constant (Kc) = [C]^3 / ([A]^2 × [B])

Plug in the values for [C], [A], and [B], and calculate the equilibrium constant.