Given a reaction, A → B + C, for which the observed rate law is rate = k[A]0, which one of the following is true?

Question

Given a reaction, A  →  B  +  C, for which the observed rate law is rate = k[A]0, which one of the following is true?

BlackTom AI · Accepted Answer

We start by identifying the given rate law and what it implies for the concentration change over time.

Option a: 1/[A]t = 1/[A]o + kt. This is the integrated rate law for a second-order reaction where the rate law is rate = k[A]^2 for a single reactant. Since the provided rate law is rate = k[A]^0, which is independent of [A], this option is not correct for a zero-order process.

Option b: 1/[A]t = 1/[A]o - kt. This form arises from integrating a rate law that is first-order in [A] (rate = k[A]). It would describe a first-order decay, not a zero-order one, so this is incorrect given the zero-order rate law.

Option c: ln[A]t = ln[A]o + kt. This is the natural-log form for a first-order reaction, where the rate is proportional to [A]. Since the rate here is independent of [A], this log form does not apply, making this option incorrect.

Option d: [A]t = [A]o + kt. This would imply that the concentration increases linearly with time, which contradicts the concept of a reaction consuming A. Therefore this is incorrect.

Option e: [A]t = [A]o - kt. This is the standard integrated rate law for a zero-order reaction, where the rate is constant (rate = k) and [A] decreases linearly with time: d[A]/dt = -k, leading to [A]t = [A]o - kt. This matches the given rate law rate = k[A]^0 = k.

Option f: ln[A]t = ln[A]o - kt. This expression would correspond to a first-order decay with a negative sign in the exponent of [A], which is not consistent with the zero-order rate law. It is therefore incorrect.

In summary, the correct interpretation of rate = k[A]^0 is a constant rate that causes a linear decrease of [A] with time, [A]t = [A]o - kt, so option e captures the proper integrated rate law for a zero-order reaction.

CHM1051 MUM S2 2025 CHM1051 Practice Exam 2

Given a reaction, A → B + C, for which the observed rate law is rate = k[A]0, which one of the following is true?

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