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

To approach this problem, I start by identifying the rate law and then apply the appropriate integrated form for a zero-order reaction.
Option a: 1/[A]t = 1/[A]o + kt. This is the integrated form for a second-order reaction where the rate law is rate = k[A]^2, not zero-order. Since our rate law is rate = k[A]^0 = k, this equation is not applicable here.
Option b: [A]t = [A]o - kt. For a zero-order reaction, the concentration of A decreases at a constant rate independent of [A]. Integrating d[A]/dt = -k gives [A]t = [A]o - kt, which matches the given scenario exactly.
Option c: [A]t = [A]o + kt. This would imply the concentration increases with time, which is physically inconsistent for a unimolecular decomposition reaction with a positive rate constant k. Therefore this cannot be correct for this process.
Option d: ln[A]t = ln[A]o - kt. This is the integrated form for a first-order reaction where rate = k[A], not for a zero-order process. Since the rate law here does not depend on [A], this first-order form is inappropriate.
Option e: 1/[A]t = 1/[A]o - kt. This expression corresponds to a particular second-order scenario (rate = k[A]^2) with a specific sign convention, not to zero-order kinetics. It does not reflect the correct integration for a zero-order rate law.
Option f: ln[A]t = ln[A]o + kt. This is also a first-order-type expression with the wrong sign convention and would not describe zero-order behavior. It incorrectly implies exponential decay rather than linear decay.
In summary, the zero-order rate law leads to a linear decrease of [A]t with time, given by [A]t = [A]o - kt, which aligns with option b. The other options correspond to different order kinetics or have incorrect signs, making them incorrect for this scenario.

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

View Explanation

Log in for full answers

Similar Questions

The reaction, 2 NO(g) + O2(g) → 2 NO2(g), was found to be first order in each of the two reactants and second order overall. The rate law should therefore be written as

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

Nitrogen dioxide decomposes via the following reaction, NO2(g) → NO(g) + 1/2O2(g) The experimental rate law is rate = k[NO2]2. At a specific temperature the rate of reaction was found to be 7.50 x 10-4 mol L-1 s-1. Which unit below is the correct unit for the rate constant in this case?

Which of the following statements is FALSE?

Which of the following statements is/are correct for the first-order reaction: A → P? I. The concentration of A decreases linearly with time. II. The rate of reaction is constant. III. A plot of ln[A] versus time is a straight line with the slope equal to -k.

Collision theory describes the factors required for an effective collision, i.e. a collision which results in a reaction. Choose the incorrect statement below.

Cyclobutane, C4H8, decomposes as shown: C4H8(g) → 2 C2H4(g). In the course of a study of this reaction, the rate of consumption of C4H8 at a certain point was 4.50 x 10-4 mol L-1 s-1. What is the rate at which C2H4(g) is being generated at this point, also in mol L-1 s-1?

The reaction, 2BrO2(g) + O2(g) → 2BrO3(g) obeys the rate law: rate = kobs[BrO2]2[O2] (where kobs is the experimentally observed rate constant). Which of the following mechanisms is consistent with the experimental rate law?

More Practical Tools for International Students

Homework AI Solver

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler