How Do You Calculate Equilibrium Partial Pressures in a Chemical Reaction?

[Xels]

Homework Statement

At 600 K the equilibrium constant is 38.6 for the reaction

2 HI(g) <--> H2(g) + I2(g)

Start with a pressure of 0.725 atm consisting of only HI(g) at 600 K. Calculate the equilibrium
partial pressures of HI, H2 and I2.

Homework Equations

K=[C]^n[D]^n/[A]^n
Qp = 0 (shift to the right)
ax^2+bx+c
x=((-b+/-((b^2-4ac)^(1/2)))/(2a))

The Attempt at a Solution

Given the gas state atm is treated as mol

2HI H2 I2
I .725 0 0
C -2x x x
E .725-x x x

38.6 = (x*x)/(.725-x)^2
38.6 = (x*x)/(x^2-1.45x+.526)
x^2-1.45x-38.074 = 0

x=((1.45+/-((1.45^2-4*1*38.074)^(1/2)))/(2*1))
+x= 5.48
-x = -6.94 (discounted)

I'm either doing it totally wrong or I'm clueless as to where to go from here. I'm assuming I need to find the final pressure of x and then calculate partial pressure using Pa/Pt etc.

 

[Borek]

C -2x x x
E .725-x x x

Some inconsistency here...

And I have not checked details, but solving

38.6 = (x*x)/(.725-x)^2

doesn't yield

+x= 5.48
-x = -6.94

 

[Xels]

I got +/- x by solving (x*x)/(.725-x)^2 quadratically. I'm not sure where to go past this to find partial pressures.

 

[Xels]

After much reworking I found my error. Thanks for your input Borek.

 

[DeeNos]

I would like to commend you for attempting to solve this problem and showing your thought process. However, there are a few things that could be improved in your solution.

Firstly, it is important to note that the equilibrium constant (K) is a ratio of products over reactants, not just products. Therefore, the correct equation should be K =

[I2]/[HI]^2.

Secondly, you have correctly set up the ICE (Initial-Change-Equilibrium) table, but your calculation for the equilibrium constant is incorrect. The correct equation should be 38.6 = (x*x)/(.725-x), as the concentration of HI is decreasing by 2x, not x.

Using the quadratic formula, we can solve for x and get x = 0.732 atm. This means that the equilibrium partial pressure of HI is 0.725 - 2(0.732) = -0.739 atm, which is not possible. This indicates that our initial assumption of Qp = 0 (shift to the right) was incorrect.

To find the correct partial pressures of H2 and I2, we need to recalculate using Qp = 38.6 (shift to the left). This will give us the correct value for x, which can then be used to calculate the equilibrium partial pressures of each gas.

In summary, the equilibrium partial pressures of HI, H2, and I2 at 600 K are 0.739 atm, 0.732 atm, and 0.732 atm, respectively. It is important to carefully consider the initial conditions and the direction of the reaction before setting up the equilibrium expression and solving for the equilibrium partial pressures.