Question

3·00 mol of PCl₅ kept in 1L closed reaction vessel was allowed to attain equilibrium at 380K. Calculate the composition of the mixture at equilibrium, K_c = 1·80.

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Solution

Let x mol of PCl₅ be dissociated.
The reaction is

PCl subscript 5 space space rightwards harpoon over leftwards harpoon space space space space space PCl subscript 3 space space plus Cl subscript 2

Initial conc. 3.0 0 0
At eqm. 3 - x x x
Applying the law of chemical equilibrium

straight K subscript straight c space equals space fraction numerator open square brackets PCl subscript 3 close square brackets space open square brackets Cl subscript 2 close square brackets over denominator open square brackets PCl subscript 5 close square brackets end fraction

...(1)
Putting the values in expression (1), we have

1.8 space equals space fraction numerator straight x squared over denominator 3 minus straight x end fraction

or space space straight x squared plus space 1.8 straight x space minus 5.4 space equals space 0 space space space space space space straight x space equals space fraction numerator open square brackets negative 1.8 space plus-or-minus square root of left parenthesis 1.8 right parenthesis squared minus 4 left parenthesis negative 5.4 right parenthesis end root close square brackets over denominator 2 end fraction space space space space space straight x space equals space fraction numerator open square brackets negative 1.8 space plus-or-minus square root of 3.24 space plus-or-minus 21.6 end root close square brackets over denominator 2 end fraction space space space space space straight x space equals space fraction numerator left square bracket 1.8 space plus-or-minus space 4.98 right square bracket over denominator 2 end fraction space or space space straight x space equals space fraction numerator left square bracket negative 1.8 space plus 4.98 right square bracket over denominator 2 end fraction space equals 1.59

therefore space space space open square brackets PCl subscript 5 close square brackets space equals space 3.0 space space minus space straight x space equals space 3.0 space minus space 1.59 space equals space 1.41 space straight M space space space space space space open square brackets PCl subscript 3 close square brackets space equals space open square brackets Cl subscript 2 close square brackets space equals space straight x space equals space 1.59 space straight M

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