Question

In the reaction, PCl_5(g)⇌PCl_3(g)+Cl_2(g) , the amounts of PCl_5, PCl_3 and Cl_2 are 2 mole each at equilibrium and the total pressure is 3 atmosphere. The equilibrium constant, K_p is

Answer must be "1 atm"

Answer 1

EXPLANATION.

PCI₅(g) ⇄ PCI₃(g) + CI₂(g).

The amount of PCI₅ & PCI₃ & CI₂ = 2 mole each at equilibrium.

Total pressure = 3 atm.

As we know that,

PCI₅(g) ⇄ PCI₃(g) + CI₂(g).

2                   2           2      at t = equilibrium.

Expression of K(p) is.

$\sf \implies K_{p} = \dfrac{\bigg(P_{PCI_3}\bigg) \bigg(P_{CI_2}\bigg)}{\bigg(P_{PCI_5}\bigg)}$

Total number of the moles = 2 + 2 + 2 = 6 moles.

$\sf \implies P_{PCI_3} = P_{T} \ \times X_{PCI_3}$

$\sf \implies P_{PCI_3} = 3 \times \dfrac{2}{6} = 1$

$\sf \implies P_{CI_2} = P_{T} \ \times X_{CI_2}$

$\sf \implies P_{CI_2} = 3 \times \dfrac{2}{6} = 1.$

$\sf \implies P_{PCI_5} = P_{T} \ \times X_{PCI_5}$

$\sf \implies P_{PCI_5} = 3 \times \dfrac{2}{6} = 1.$

$\sf \implies K_{p} = \dfrac{\bigg(P_{PCI_3}\bigg) \bigg(P_{CI_2}\bigg)}{\bigg(P_{PCI_5}\bigg)} = \dfrac{1 \times 1}{1} = 1 \ atm.$

                                                                                                                           

MORE INFORMATION.

Summary various homogenous equilibrium.

(1) = H₂ + I₂ ⇄ 2HI.

(2) = N₂ + O₂⇄ 2NO

⇒ Δn = 0.

⇒ ΔH = +QK cal (endothermic) K(p) = Kc.

⇒ Kc = 4x²/(a - x)(b - x)

⇒ K(p) = 4x²/(a - x)(b - x).

Helping factors = to obtain ↑ NO & HI.

⇒ (a) = high temperature.

⇒ (b) = [N₂] & [O₂] ↑.

⇒ (c) = p → no effect.

Answer 2

Required Answer :-

Pressure = 3 atom

No. of mole = 2 + 2 + 2 = 6 moles

By using the formula

$\bf P_{PCI3} = Pressure\times\dfrac{Mole \; in \; 1 \; substance}{Total moles}$

$\sf P_{PCI3} = 3 \times\dfrac{2}6$

$\sf P_{PCI3} = \dfrac{2}{2}$

$\sf P_{PCI3} = 1$

Again using same formula

$\bf P_{PCI2} = Pressure\times\dfrac{Mole \; in \; 1 \; substance}{Total moles}$

$\sf P_{PCI2} = 3 \times\dfrac{2}6$

$\sf P_{PCI2} = \dfrac{2}{2}$

$\sf P_{PCI2}= 1$

Again using same

$\bf P_{PCI5} = Pressure\times\dfrac{Mole \; in \; 1 \; substance}{Total moles}$

$\sf P_{PCI5} = 3 \times\dfrac{2}6$

$\sf P_{PCI5} = \dfrac{2}{2}$

$\sf P_{PCI5}= 1$

Now

$\bf Equilibrium\; constant = \dfrac{P_{PCI2} \times P_{PCI3}}{P_{PCI5}}$

$\sf Equilibrium \; constant = \dfrac{1\times 1}{1}$

$\sf Equilibrium \; constant = \dfrac{1}{1}$

$\bf\red{Equilibrium \; constant = 1 \; atom}$