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.