Method for getting correct answer for this? Thank you!

For the reaction A ↔ 2B K = 3.80x10-7 , if one started with 0.154 M A approximately how much A and B would there be after equilibrium had been established?

a. very little A, 0.154 M B

b. 0.126 M A; 0.027 M B

c. 0.154 M A, very little B

d. 0.027 M A; 0.126 M B

.........A ==> 2B

I....0.154.....0
C........-x....2x
E...0.154-x....2x

Substitute the E line into Kc expression and solve for x and 0.154-x.

I don't know if the prof expects you to answer this with math (working out the above equation) or by reason but the math should do it but take more time. I suspect the answer is c but I didn't go through the math. None of the others can be right so c is elected by elimination of the others.

To determine the concentrations of A and B at equilibrium, you can use the equilibrium constant expression and set up an ICE table.

1. Write the balanced equation for the reaction: A ↔ 2B.

2. Set up an ICE table. This table helps you track the changes in the concentrations of reactants and products during the reaction.

- Start with the initial concentration of A, which is given as 0.154 M.
- Assume that x moles of A react and form 2x moles of B.
- The change in concentration of A is -x, and the change in concentration of B is +2x.
- The equilibrium concentrations of A and B can be expressed as: [A] = 0.154 - x and [B] = 2x.

| | Initial | Change | Equilibrium |
|-------|---------|--------|-------------|
| A | 0.154 M | -x | 0.154 - x |
| B | 0 M | +2x | 2x |

3. Write the expression for the equilibrium constant, K:

K = [B]^2 / [A]

Substitute the equilibrium concentrations of A and B into the expression:

K = (2x)^2 / (0.154 - x)

4. Substitute the given value for K (3.80 × 10^-7) into the expression and solve for x.

3.80 × 10^-7 = (2x)^2 / (0.154 - x)

Solve this equation to find the value of x.

5. Once you have found the value of x, substitute it back into the equilibrium concentrations of A and B to determine their values.

[A] = 0.154 - x
[B] = 2x

6. Compare the calculated concentrations of A and B to the answer choices provided to find the correct option.

In this case, the correct answer would be (b): 0.126 M A; 0.027 M B.