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At 540 K, 0.10 mole of PCl5 are heated i...

At `540 K, 0.10` mole of `PCl_5` are heated in a 8 litre flask. The pressure of the equilibrium mixture is found to be 1.0 atm. The value of `K_p` (in atm) for the reaction is

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The correct Answer is:
1.77
`{:("Given equilibrium",PCl_5, Vol. of container = 8 litre
Total no. of moles = `0.1 - x + x + x = 0.1 + x`
`K_c = ([PCl_3][Cl_2])/([PCl_5]) = (x//8.x//8)/(((0.1 - x)/(8))) = (x^2)/(8(0.1 - x))`
`PV = nRT`
or , `1 xx 8 = (0.1 + x) xx 0.082 xx 540`
`therefore x = 0.08`
`therefore K_C = (0.08 xx 0.08)/(8(0.1 - 0.08)) = 4 xx 10^(-2) "mol litre"^(-1)`
`K_p = K_c (RT)^(Deltan), Deltan = +1`
`therefore K_p = 4 xx 10^(-2) (0.082 xx 540) = 1.77 atm`.
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