Q1(f). Zero-order integrated law

Answer in brief

[A]ₜ=[A]₀-kt; the half-life is [A]₀/(2k).

Key points

• In a zero-order regime, -d[A]/dt=k, independent of reactant concentration. Integrating from [A]₀ to [A]ₜ and time 0 to t gives [A]ₜ-[A]₀=-kt.
• A concentration–time plot is linear with slope -k and intercept [A]₀. The rate constant has concentration/time units.
• Setting [A]ₜ=[A]₀/2 gives t_(1/2)=[A]₀/(2k); unlike a first-order half-life, this depends on the starting concentration.
• A saturated enzyme reaction is approximately zero order in substrate when [S]≫ K_M, since v=Vₘₐₓ[S]/(K_M+[S])≈ Vₘₐₓ.