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At 25°C, K = 0.090 for the following reaction. H2O(g) + Cl2O(g) equilibrium reaction arrow 2 HOCl(g) Calculate the concentrations of all species at equilibrium for each of the following cases. (a) 1.3 g H2O and 2.2 g Cl2O are mixed in a 1.5-L flask.

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Edufirst

Answer:

  • [HOCl] = 0.00909 mol/liter
  • [Hâ‚‚O] = 0.03901 mol/liter
  • [Clâ‚‚O] = 0.02351 mol/liter

Explanation:

1. Chemical reaction:

[tex]H_2O(g)+Cl_2O(g)\rightleftharpoons 2 HOCl(g)[/tex]

2. Initial concentrations:

i) 1.3 g Hâ‚‚O

  • Number of moles = 1.3g / (18.015g/mol) = 0.07216 mol
  • Molarity, M = 0.07216 mol / 1.5 liter = 0.0481 mol/liter

ii) 2.2 g Clâ‚‚O

  • Number of moles = 2.2 g/ (67.45 g/mol) = 0.0326 mol
  • Molarity = 0.0326mol / 1.5 liter = 0.0217 mol/liter

3. ICE (Initial, Change, Equilibrium) table

            [tex]H_2O(g)+Cl_2O(g)\rightleftharpoons 2 HOCl(g)[/tex]

I            0.0481      0.0326            0

C              -x                 -x              +x

E          0.0481-x    0.0326-x         x

4. Equilibrium expression

       [tex]K_c=\dfrac{[HOCl]^2}{[H_2O].[Cl_2O]}[/tex]

     [tex]0.09=\dfrac{x^2}{(0.0481-x)(0.0326-x)}[/tex]

5. Solve:

            [tex]x^2=0.09(x-0.0481)(x-0.0326)\\\\0.91x^2+0.007263x-0.000141125=0[/tex]

Use the quadatic formula:

[tex]x=\dfrac{-0.007263\pm \sqrt{(0.007263)^2-4(0.91)(-0.000141125)}}{2(0.91)}[/tex]

The positive result is x = 0.00909

Thus the concentrations are:

  • [HOCl] = 0.00909 mol/liter
  • [Hâ‚‚O] = 0.0481 - 0.00909 = 0.03901 mol/liter
  • [Clâ‚‚O] = 0.0326 - 0.00909 = 0.02351 mol/liter

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