Question

When `PCl_(5)` is heated, it dissociates into `PCl_(3)` and `Cl_(2)`. The vapour density of the gas mixture at `200^(@)C` and at `250^(@)C` is `70` and `58`, respectively. Find the degree dissociation at two temperatures.

Answer 1

`PCl_(5)(g)hArrPCl_(3)(g)+Cl_(2)(g)`

Total "moles" `=a+aalpha`
Using the result `=[d_(0)/d_(mix)=(a+aalpha)/a]`
`d_(0)`= density of `PCl_(5)`
At `T=200^(@)C, (vd -= "vapour density")`
`rArr d_(0)/d_(mix)=(vd_(PCl_(5)))/(vd_(mix))=(M_(0)//2)/(70)=(a+aalpha)/a=(208.5//2)/70=1+alpha`
`:. alpha=0.49`
At `T=250^(@)C`
`d_(0)/d_(mix)=(vd_(PCl_(5)))/(vd_(mix))=(M_(0)//2)/(58)=(a+aalpha)/a`
`=(208.5//2)/58=1+alpha rArr alpha=0.80`