The kinetics of a first order reaction A B are studied by plotting ₁₀[A] versus time t (in minutes). The plot yields a straight line with a slope of -0.01 min ⁻¹ . The time required for 99 % completion of the reaction is _____ min.

Step-by-step solution

The integrated rate law for a first order reaction is: [A] = [A]₀ - kt Converting to base 10 logarithm: ₁₀[A] = ₁₀[A]₀ - k 2.303 t The slope of the plot of ₁₀[A] versus t is - k 2.303 . Given slope = -0.01 min ⁻¹ : - k 2.303 = -0.01 k = 0.02303 min ⁻¹ For 99 % completion, the amount of reactant remaining is 1 % of the initial amount, so [A]_t = 0.01 [A]₀ . The time t required is: t = 2.303 k ₁₀ ( [A]₀ [A]_t ) t = 2.303 0.02303 ₁₀ ( 100 1 ) t = 100 2 = 200 min Answer: 200