A first order reaction take 30 minutes for 75 % decomposition, calculate its rate constant ?

Step-by-step solution

For a first order reaction, the integrated rate law is given by: k = 2.303 t ( a a-x ) Given that the reaction is 75 % complete in 30 minutes: t = 30 minutes x = 0.75a a - x = a - 0.75a = 0.25a Substituting these values into the rate equation: k = 2.303 30 ( a 0.25a ) k = 2.303 30 (4) k = 2.303 30 0.6020 k = 1.386 30 = 0.0462 minute ⁻¹ Alternatively, 75 % decomposition corresponds to two half-lives: t_ 75 % = 2 t_ 1/2 30 = 2 t_ 1/2 t_ 1/2 = 15 minutes k = 0.693 t_ 1/2 = 0.693 15 = 0.0462 minute ⁻¹ The closest given