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The degree of dissociation of PCl 5 at 1 atm is 0.2. Calculate the pressure at which PCl 5 is dissociated to 50%

The degree of dissociation of PCl5 at 1 atm is 0.2. Calculate the pressure at which PCl5 is dissociated to 50%

Grade:12

1 Answers

Pankaj
askIITians Faculty 131 Points
9 years ago
PCl5↔ PCl3 + Cl2
If α is the degree ofdissociation , then
Initial concentration:
PCl5= 1
PCl3= 0
Cl2= 0
At Equilibrium:
PCl5= 1 – α
PCl3= α
Cl2= α
Totalnumberofmolesat equilibrium = 1 – α + α + α = 1 + α
Partial pressuresof PCl5, PCl3and Cl2will be:
p (PCl3) = α p / 1 + α
p (Cl2) = α p / 1 + α
p (PCl5) = (1 – α) p / 1 + α
Kp= p (PCl3) X p (Cl2) / p (PCl5)
Kp=[(α p / 1 + α) X (α p / 1 + α)]/[(1 – α) p / (1 + α)]
= α2p / (1 – α)2
Substituting p = 1 atm and α = 0.2
Kp= (0.2)2X 1 / (1 – (0.2))2
= 0.041
When α = 1/2 = 0.5, let pressure is p’
Kp= α2p’/ (1 – α)2
0.041 = (0.5) sup>2 p’/ (1 – (0.5))2
p’= (0.041) [1 – (0.5)2] / (0.5)2
p’= 0.125 atm

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