Answer : The equilibrium constant kc is 4.76 x 10⁻³
Explanation :
The given equilibrium reaction is
![2SO_{3} (g) \leftrightarrow 2SO_{2} (g) + O_{2} (g)](https://tex.z-dn.net/?f=2SO_%7B3%7D%20%28g%29%20%5Cleftrightarrow%202SO_%7B2%7D%20%28g%29%20%2B%20O_%7B2%7D%20%28g%29)
Step 1 : Set up ICE table
Let us set up an ICE table for this reaction .
The initial concentration of SO₃ is
![Concentration = \frac{mol}{L} = \frac{0.740mol}{4L} = 0.185 M](https://tex.z-dn.net/?f=Concentration%20%3D%20%5Cfrac%7Bmol%7D%7BL%7D%20%3D%20%5Cfrac%7B0.740mol%7D%7B4L%7D%20%3D%200.185%20M%20)
The initial concentrations of products are 0.
Let us assume x is the change .
Please refer the attached picture.
Step 2 : Use the given value to find x
From the ICE table, we can see that at equilibrium, concentration of O₂ is x
But we have been given that , at equilibrium we have 0.190 mol of O₂ .
Let us convert this to concentration unit.
Concentration of O₂ at equilibrium = ![\frac{mol}{L} = \frac{0.190mol}{4L} = 0.0475 M](https://tex.z-dn.net/?f=%5Cfrac%7Bmol%7D%7BL%7D%20%3D%20%5Cfrac%7B0.190mol%7D%7B4L%7D%20%3D%200.0475%20M)
But concentration of O₂ from the ICE table is x.
Therefore we have x = 0.0475 M
Step 3 : Using x , find equilibrium concentrations
Using this value, let us write the equilibrium concentrations of the given species.
[SO₃]eq = 0.185 M - 2x = 0.185 - 2(0.0475) = 0.09 M
[SO₂]eq = 2x = 0.095 M
[O₂]eq = x = 0.0475 M
Step 4 : Set up equation for kc and solve it
The equilibrium constant kc is calculated as,
![k_{c} = \frac{[SO_{2}]^{2} [O_{2}]}{[SO_{3}]^{2}}](https://tex.z-dn.net/?f=k_%7Bc%7D%20%3D%20%5Cfrac%7B%5BSO_%7B2%7D%5D%5E%7B2%7D%20%5BO_%7B2%7D%5D%7D%7B%5BSO_%7B3%7D%5D%5E%7B2%7D%7D)
Let us plug in the above equilibrium values.
![k_{c} = \frac{(0.095)^{2} (0.0475)}{(0.09)^{2}}](https://tex.z-dn.net/?f=k_%7Bc%7D%20%3D%20%5Cfrac%7B%280.095%29%5E%7B2%7D%20%280.0475%29%7D%7B%280.09%29%5E%7B2%7D%7D)
![k_{c} = \frac{0.00042869}{0.09}](https://tex.z-dn.net/?f=k_%7Bc%7D%20%3D%20%5Cfrac%7B0.00042869%7D%7B0.09%7D)
![k_{c} = 4.76 \times 10^{-3}](https://tex.z-dn.net/?f=k_%7Bc%7D%20%3D%204.76%20%5Ctimes%2010%5E%7B-3%7D)
The equilibrium constant kc is 4.76 x 10⁻³