Prove $a = \sqrt{\frac{K_{p}}{P + K_{p}}}$ for $P C l_{5} ⇌ P C l_{3}$ + $C l_{2}$ , where $a$ is degree of dissociation at temperature when equilibrium constant is $K_{p}$ .

Open in App

Solution

$P {C l}_{5} ⇌ {P C l}_{3} + {C l}_{2}$
Initial moles $\to$ $1$ $0$ $0$
At equation $\to$ $1 - α$ $α$ $α$
$α =$ Degree of Dissociation.
Total moles $= 1 + α$
$K_{p} = \frac{(\frac{α}{1 + α}) P . (\frac{α}{1 + α}) P}{(\frac{1 - α}{1 + α}) P}$
$P =$ Equilibrium Pressure
$K_{p} = \frac{α^{2}}{1 - α^{2}} . P \frac{K_{p}}{P} = \frac{α^{2}}{1 - α^{2}} α^{2} = \frac{K_{p}}{K_{p} + P}, α = \sqrt{\frac{K_{p}}{K_{p} + P}}$

Suggest Corrections

Similar questions

α = {[K_{p} / (P + K_{p})]}^{1 / 2}

for

P C l_{5} ⇌ P C l_{3} + C l_{2}

; where,

α

is degree of dissociation at temperature when equilibrium constant is .

Q. The degree of dissociation of

P C l_{5}

at a certain temperature and

1 a t m

pressure is

0.20

. Calculate the value of equilibrium constant

K_{p}

Q. The degree of dissociation of

P C l_{5}

at a certain temperature and pressure=

1 a t m

is 0.20. Calculate the value of equilibrium constant

K_{p}

Q. At

250^{o} C

and 1 atm presser the V.d of

P C l_{5}

is 57.9
calculate PCl

⇌ P C l_{3} + C l_{2}

I Kp of rxn
II % dissociation when p is doubled

At $227^{o} C$ one mole of $C l_{2}$ and 3 moles of $P C l_{5}$ are placed in a 100 litre container and allowed to reach equilibrium. It is found that the equilibrium pressure is 2.05 atmospheres. Assuming ideal behaviour, the degree of dissociation 'x' for $P C l_{5}$ and $K_{p}$ for the reaction $P C l_{5}$ (g) $⇌$ $P C l_{3}$ (g) + $C l_{2}$ (g) is:

Join BYJU'S Learning Program

Prove a=√KpP+Kp for PCl5⇌PCl3 +Cl2, where a is degree of dissociation at temperature when equilibrium constant is Kp.

PCl5⇌PCl3+Cl2Initial moles → 1 0 0At equation → 1−α α αα= Degree of Dissociation.Total moles=1+αKp=(α1+α)P.(α1+α)P(1−α1+α)P P= Equilibrium PressureKp=α21−α2.PKpP=α21−α2α2=KpKp+P,α=√KpKp+P

Prove $a = \sqrt{\frac{K_{p}}{P + K_{p}}}$ for $P C l_{5} ⇌ P C l_{3}$ + $C l_{2}$ , where $a$ is degree of dissociation at temperature when equilibrium constant is $K_{p}$ .