Kp=1.6
Kp=1.0*10^-4
A<->2B
Find the equilibrium partial pressures of A and B
B=1.0 atm
A=0.0 atm
This is what I have so far
A 2B
0 1.0
+p -p
p 1-p
[B]^2/A (1-p)^2/p = 1.6
then got a quadratic equation of p^2+1.6p-1 to get x=.48
Look at your algebra. I did that and obtained p^2 - 3.6p + 1.0 = 0
Not sure what I did there? my x value came to be .3035. Should I plug this number into the (1-p)^2/p
if that is correct then i got a value of 1.6 after plugging it in. This is the step that Im not sure what to do.
I get 0.48 if I solve p^2 + 1.6p -1 = 0
If I solve p^2 -3.6p + 1 = 0 I get 0.303
I got the same answers for both, but I don't know how to get two pressures from these numbers
p (your x) = 0.303 = partial pressure of A.
1-0.303 = ? = partial pressure of B.
That is if you are going with 0.303 for p.
To find the equilibrium partial pressures of A and B in the given reaction, you can use the equilibrium constant expression and the initial conditions.
The equilibrium constant expression (Kp) for the reaction A <-> 2B is given as 1.6. We also have the initial pressures:
[A] = 0.0 atm (initial partial pressure of A)
[B] = 1.0 atm (initial partial pressure of B)
Now, let's assume the change in partial pressure of A to be "x," which means the equilibrium partial pressure of A would be (0 + x) = x atm.
The change in partial pressure of B, since it is a product in the reaction, would be -2x, and the equilibrium partial pressure of B would be (1.0 - 2x) atm.
Substituting these values into the equilibrium constant expression, we get:
([B]^2 / [A]) = [(1.0 - 2x)^2 / x]
Now, setting this expression equal to the given value of Kp (1.6), we can write the equation:
[(1.0 - 2x)^2 / x] = 1.6
To solve this equation, we need to rearrange it to a quadratic form:
(1.0 - 2x)^2 = 1.6x
Expanding and simplifying:
1 - 4x + 4x^2 = 1.6x
Rearranging to a quadratic equation:
4x^2 - 5.6x + 1 = 0
Now, you can solve this quadratic equation to find the value of x, which represents the change in partial pressure of A at equilibrium. Once you have the value of x, you can calculate the equilibrium partial pressures of A and B by substituting it back into the expressions we assumed earlier.
I hope this helps you in finding the equilibrium partial pressures of A and B! Let me know if you need further assistance.