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Question

# In equilibrium reaction, x moles of the reactant A decompose to give 1 mole each of C and D. If the fraction of A decomposed at equilibrium is independent of initial concentration, then the value of x would be:

A
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B
2
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C
3
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D
4
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Solution

## The correct option is A 2The fraction of A decomposed at equilibrium is independent of initial concentration.This implies that the concentration term is not present in the equilibrium constant expression.The equilibrium reaction is xA⇌C+D.Let the inital concentration of A be c M.The equilibrium concentrations of A,C and D are c(1−a),cαx and cαx respectively.The expression for the equilibrium constant is KC=[C][D][A]x=(cαx)×(cαx)[c(1−α)]x=(cα)2x2[c(1−α)]x.When x=2, the equilibrium constant expression will be free from the concentration term.Hence, KC=c2α24[c(1−α)]2=α24(1−α)2.Thus, option B is correct.

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