For a first order reaction A Products t/ min % of reactant decomposed 0 0 x 90 60 99.9 The value of x is ______ .

Step-by-step solution

For a first order reaction, the integrated rate law is: k = 1 t [A]₀ [A]_t At t = x min, 90 % of the reactant has decomposed, so 10 % remains. Thus, [A]_x = 0.1 [A]₀ . k = 1 x 100 10 = 1 x 10 At t = 60 min, 99.9 % of the reactant has decomposed, so 0.1 % remains. Thus, [A]₆₀ = 0.001 [A]₀ . k = 1 60 100 0.1 = 1 60 1000 = 3 60 10 Equating the two expressions for k : 1 x 10 = 3 60 10 1 x = 1 20 x = 20 Answer: 20