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KCET2010ChemistryChemical Equilibrium

Consider the following gaseous equilibria with equilibrium constants K ₁ and K ₂ respectively. aligned SO ₂( ~g )+& 1 2 O ₂( ~g ) SO ₃( ~g ) 2 SO ₃(g) & 2 SO ₂(g)+ O ₂(g) aligned The equilibrium constants are related as

Options

  1. AK ₁²= 1 ~K ₂
  2. B2 ~K ₁= K ₂²
  3. CK ₂= 2 ~K ₁²
  4. DK ₂²= 1 ~K ₁

Correct answer

A. K ₁²= 1 ~K ₂

Step-by-step solution

For the reaction, aligned & SO ₂( ~g )+ 1 2 O ₂( ~g ) SO ₃( ~g ) & Equilibrium constant, K ₁= [ SO ₃ ] [ SO ₂ ] [ O ₂ ]^ 1 / 2 (i) aligned For the reaction, aligned &2 SO ₃( ~g ) 2 SO ₂( ~g )+ O ₂( ~g ) & equilibrium constant, K ₂= [ SO ₂ ]² [ O ₂ ] [ SO ₃ ]² (ii) aligned On squaring both sides in Eq (i), we get K ₁²= [ SO ₃ ]² [ SO ₂ ]² [ O ₂ ] (iii) Eqs. (ii) Eq (iii), we get K ₁² K ₂=1 or aligned K ₂ &= 1 ~K ₁² ~K ₁² &= 1 ~K ₂ aligned

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