Equilibrium concentration of HOCl at 25°C is 0.140 M
The equation of the reaction at equilibrium is given below:
H₂O (g) + Cl₂O (g) ⇄ 2 HOCl (g)
Equilibrium constant, Kc = 0.0900 at 25°C
An ICE chart for the reaction is set up below
H₂O (g) + Cl₂O (g) ⇄ 2 HOCl (g)
I 0.384 0.384 0.652
C -x -x + 2x
E 0.384 - x 0.384 - x 0.652 + 2x
The equation of the equilibrium constant is given as;
Kc = [tex]\frac{[HOCl]^2}{[H_{2}O][Cl_{2}O]}[/tex]
substituting the values into the equation:
Kc = [tex]\frac{(0.652 + 2x)^2}{( 0.384 - x)( 0.384 - x)}[/tex] = 0.0900
4x² + 2.608x + 0.425 = 0.0900 (0.147 - 0.768x + x²)
4x² - 0.09x² + 2.677x - 0.069x + 0.425 - 0.013 = 0
3.910x² + 2.677x + 0.412 = 0
Solving using the quadratic formula:
a = 3.910, b = 2.677, c = 0.412
x = [tex]\frac{-2.677\±\sqrt{2.677^2 - 4*3.910*0.412}}{2*3.910}[/tex]
x = -0.256 or -0.431
The negative sign indicates that equilibrium is to the left of the reaction
Since x cannot be greater than 0.384, x = -0.256.
Equilibrium concentration of HOCl = 0.652 + 2(-0.256)
Equilibrium concentration of HOCl at 25°C is 0.140 M
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