The rate constant for a first order reaction is 60 s ⁻¹ . How much time will it take to reduce the concentration of the reactant to 1/20^ th of its initial value?

Step-by-step solution

For a first order reaction, the time required is given by the integrated rate equation: t = 2.303 k ( [R]₀ [R] ) Given k = 60 s ⁻¹ and the final concentration [R] = [R]₀ 20 . Substituting the values into the equation: t = 2.303 60 ( [R]₀ [R]₀ 20 ) t = 2.303 60 (20) Using (20) = (2 10) = 2 + 10 = 0.3010 + 1 = 1.3010 : t = 2.303 1.3010 60 t = 2.9962 60 t 0.0499 s Answer: 0.0499 s