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JEE MainChemistryChemical Kinetics

The kinetics of a first order reaction is studied by plotting ₁₀[ A ] against time t in minutes. The plot is a straight line with a slope of -0.01505 min ⁻¹ . The time required for 87.5 % completion of the reaction is ________ min. (Nearest integer) Given : ₁₀ 2 = 0.3010

Correct answer

60

Step-by-step solution

For a first order reaction, the integrated rate law is: ₁₀[ A ] = ₁₀[ A ]₀ - k 2.303 t Comparing this with the equation of a straight line, the slope is: Slope = - k 2.303 = -0.01505 min ⁻¹ The half-life of the reaction is given by: t_ 1/2 = 0.693 k = 2.303 ₁₀ 2 k Substituting 2.303 k = 1 0.01505 : t_ 1/2 = 0.3010 0.01505 = 20 min For 87.5 % completion, the amount of reactant remaining is: 100 % - 87.5 % = 12.5 % Fraction remaining = 12.5 100 = 1 8 = ( 1 2 )^3 This corresponds to 3 half-lives. Time required = 3 t_

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