If for a first-order reaction, [A]₀ = 1.0 M and [A]_t = 0.25 M after 276 s, find the value of the rate constant (k).

Step-by-step solution

For a first-order reaction, the concentration after n half-lives is given by [A]_t = [A]₀ 2^n . Given [A]₀ = 1.0 M and [A]_t = 0.25 M , we have: 0.25 = 1.0 2^n 2^n = 4 n = 2 Thus, two half-lives have passed in 276 s . 2 t_ 1/2 = 276 s t_ 1/2 = 138 s The rate constant k is given by: k = 0.693 t_ 1/2 = 0.693 138 k 0.0050 s ⁻¹