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JEE MainChemistryChemical Kinetics

Consider the reaction: X + Y Z It is observed that the half-life of X becomes half when its initial concentration is doubled. Also, when the rate of the reaction is plotted against the concentration of Y , the resulting graph is a straight line passing through the origin. The overall order of the reaction is _______

Correct answer

3

Step-by-step solution

The relationship between half-life ( t_ 1/2 ) and initial concentration ( [A]₀ ) for an n^ th order reaction is given by: t_ 1/2 1 [A]₀^ n-1 Since the half-life of X becomes half when its initial concentration is doubled, we have: 1 2 = ( 1 2 )^ n-1 n - 1 = 1 n = 2 Thus, the order of the reaction with respect to X is 2 . For reactant Y , the plot of rate versus [ Y ] is a straight line passing through the origin. This implies: Rate [ Y ]^1 Thus, the order with respect to Y is 1 . The overall order of the reaction i

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