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Consider the following equilibrium reactions at a certain temperature: (i) N ₂( g ) + O ₂( g ) 2 NO ( g ) ; K₁ (ii) NO ( g ) + 1 2 O ₂( g ) NO ₂( g ) ; K₂ The equilibrium constant K₃ for the reaction 2 NO ₂( g ) N ₂( g ) + 2 O ₂( g ) in terms of K₁ and K₂ is:

Options

  1. AK₃ = 1 K₁ + K₂^2
  2. BK₃ = 1 K₁ K₂
  3. CK₃ = 1 K₁ K₂^2
  4. DK₃ = K₁ K₂^2

Correct answer

C. K₃ = 1 K₁ K₂^2

Step-by-step solution

The target reaction is: 2 NO ₂( g ) N ₂( g ) + 2 O ₂( g ) To obtain this target reaction, we manipulate the given reactions as follows: Reverse reaction (i). The equilibrium constant becomes the reciprocal of K₁ . 2 NO ( g ) N ₂( g ) + O ₂( g ) ; K' = 1 K₁ Reverse reaction (ii) and multiply it by 2. The equilibrium constant becomes the reciprocal of K₂ , raised to the power of 2. 2 NO ₂( g ) 2 NO ( g ) + O ₂( g ) ; K'' = ( 1 K₂ )^2 = 1 K₂^2 Add the two modified reactions. [2 NO ( g ) N ₂( g ) + O ₂( g ) ] + [2 NO ₂

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