Answer :The correct order for equilibrium constant = K₁ > K₂ >K₃
Ethene is an alkene and X2 is elemental halogen . The reaction between alkene and halogen is known as Halogenation reaction . This reaction involves electrophilic addition mechanism . In this reaction elemental halogen (X₂ ) produces a elctrophile , X⁺ . This electrophile is attracted by the double bond in alkene and attached to it .
Due to addition of electrophile , it produces carbocation intermediate .On this positive carbon , nucleophile attacks , hence , a resultant 1,2-di halide alkane is produced .( in image )
The reaction between ethene ( C₂H₄) and halogen ( X₂) produces 1,2 - dihalide ethane (C₂H₄X₂) . The image shows reaction between chlorine ,Cl₂ , a halogen (X₂) .
The expression for equilibrium constant of reaction between ethene and halogen is given as:
[tex] K = \frac{product}{reactant } [/tex]
Product = C₂H₄X₂ Reactants = C₂H₄ and X₂
[tex] K = \frac{[C_2H_4X_2]}{[C_2H_4] [X_2]} [/tex]
On applying this concept in figures :
Given : Green = Cl₂ Brown = Br₂ Purple = I₂ Grey = Ethene
Grey + Green = 1,2- dihalide ethane
a) Number of Cl₂(green ) = 2
number of ethane ( grey ) = 2
Number of 1,2-dichloride alkane( grey + green ) = 8
Plugging these number in equilibrium constant expression :
[tex] K_1 = \frac{8}{2 * 2 } = \frac{8}{4} = 2 [/tex]
Hence K₁ for ethene + chlorine = 2
b) Number of Br₂(brown ) = 4
number of ethane ( grey ) = 4
Number of 1,2-dibromide alkane( grey + brown ) = 6
On plugging these values in K expression as :
[tex] K_2= \frac{6 }{4 * 4 } = \frac{6}{16} = 0.375 [/tex]
Hence K₂ for ethen + Bromine = 0.375
c) Number of I₂(purple ) = 7
number of ethane ( grey ) = 7
Number of 1,2-diiodide alkane( grey + purple ) = 3
On plugging values in K expression as:
[tex] K_3 = \frac{3}{7 * 7 } = \frac{3}{49} = 0.0612 [/tex]
Hence K₃ for ethene + Iodine = 0.0612
So , the order of equilibrium constant (K) from largest to smallest :
K₃ = 0.0612 K₂ = 0.375 K₁= 2
K₁ > K₂ >K₃
