Two separate vessels initially contain A at the same concentration c₀. One follows zero-order disappearance and the other first-order disappearance; their half-lives are equal to τ. At t = τ/2, what i

Question

Two separate vessels initially contain A at the same concentration c₀. One follows zero-order disappearance and the other first-order disappearance; their half-lives are equal to τ. At t = τ/2, what is the ratio of instantaneous disappearance rate in the first-order vessel to that in the zero-order vessel?

TestHub · Accepted Answer

Equal half-lives give k₀ = c₀/(2τ) and k₁ = (ln 2)/τ. At t = τ/2, the first-order concentration is c₀exp[-(ln 2)/2] = c₀/√2, so its rate is c₀ln 2/(τ√2). The zero-order rate is still k₀ = c₀/(2τ), because depletion occurs only at 2τ. Dividing gives 2ln 2/√2 = √2 ln 2. Equal half-lives do not make instantaneous rates equal, and the initial rate ratio 2ln 2 has already fallen by a factor √2 at this instant.

Chemistry - Chemical Kinetics Question with Solution | TestHub

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