If the rate constant for a first order reaction is 2 . 303 × 10 - 3 s - 1 , find the time required to reduce 4 g of the reactant to 0 . 2 g .

Step-by-step solution

According to the integrated rate law for the rate of reaction, the rate constant is: k = 1 t ln a a - x Rate constant k = 2 . 303 × 10 - 3   s - 1 Weight of reactant at t = 0 is 4   g . Weight after the time t = t is 0 . 2 g . t = 1 k ln a a - x = 1 2 . 303 × 10 - 3   s - 1 ln 4 0 . 2 = 434 . 22 × ln 20 = 434 . 22 × 2 . 996   s = 1300 . 92   s t = 1300 . 92   s = 1300 . 92 3600 = 0 . 36   hour So, the time required is 0 . 36 hours.