Calculate the number of moles of Cl2 produced at equilibrium when 3.98 mol of PCl5 is heated at 283.9 deg celsius in a vessel having a capacity of 10.0L. At 283.9, K = 0.060 for this dissociation.

1.274 moles

Explanation:

The equation for the reaction can be represented as follows:

                                  ⇄           +        

K = 0.060

K =

Concentration of    =

Concentration of    =

Concentration of    = 0.398 moles

If we construct an ICE table for the above equation; we have:

                                  ⇄           +        

Initial                0.398                          0                          0

Change            - x                               + x                        + x

Equilibrium    (0.398 - x)                      x                          x

K =

K =

K =

0.060 =

0.06(0.398-x) = x²

0.02388 - 0.060x = x²

x² + 0.060x - 0.02388 = 0               (quadratic equation)

a = 1;       b= 0.06;      c= -0.02388

Using quadratic formula;

=  

=

=

=

=

=   or

=  or

= 0.1274 or -0.1874

We go by the positive value which says:

[x] = 0.1274 M

number of moles = 0.1274 × 10.0

= 1.274 moles

∴ the number of moles  of Cl₂ produced at equilibrium = 1.274 moles

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