To calculate the concentrations of all species at equilibrium, we need to set up an ICE (Initial, Change, Equilibrium) table. Here's how you can do it step by step:
Step 1: Write the balanced equation for the reaction
H2O(g) + Cl2O(g) ⇌ 2 HOCl(g)
Step 2: Set up the ICE table
Species Initial (mol/L) Change (mol/L) Equilibrium (mol/L)
HOCl ? -2x 1.3 - 2x
Cl2O ? -x
H2O ? -x
Step 3: Apply the equilibrium expression and expression for K
The equilibrium expression for this reaction is:
K = ([HOCl]^2) / ([Cl2O] * [H2O])
Given that K = 0.090 at 25°C, we can set up the equation:
0.090 = (1.3 - 2x)^2 / (x * x)
Step 4: Solve for x
Solve the equation for x by rearranging and solving the quadratic equation:
0.090 * x^2 = (1.3 - 2x)^2
0.090 * x^2 = 1.69 - 5.2x + 4x^2
0.010x^2 + 5.2x - 1.6881 = 0
You can solve this quadratic equation using a calculator or any other preferred method. Once you find the value of x, you can substitute it back into the ICE table to determine the equilibrium concentrations.
Step 5: Calculate the concentrations at equilibrium
[HOCl] = 1.3 - 2x (substitute the value of x)
[Cl2O] = -x (substitute the value of x)
[H2O] = -x (substitute the value of x)
Calculating the concentrations based on the determined value of x will give you the final values for each species at equilibrium.
Remember to convert the final concentration values to mol/L if necessary.
I hope this explanation helps you understand how to solve this equilibrium problem! Let me know if you have any further questions.