Three different reactions involve a single reactant converting to products. Reaction A has a half-life that is independent of the initial concentration of the reactant, reaction \(\mathrm{B}\) has a half-life that doubles when the initial concentration of the reactant doubles, and reaction \(\mathrm{C}\) has a half-life that doubles when the initial concentration of the reactant is halved. Which state- ment is most consistent with these observations? a. Reaction A is first order; reaction \(\mathrm{B}\) is second order; and reaction C is zero order. b. Reaction A is first order; reaction \(\mathrm{B}\) is zero order; and reaction C is zero order. c. Reaction A is zero order; reaction B is first order; and reaction C is second order. d. Reaction \(\mathrm{A}\) is second order; reaction \(\mathrm{B}\) is first order; and reaction C is zero order.

Short Answer

Expert verified
The correct answer is a. Reaction A is first order; reaction B is second order; and reaction C is zero order.

Step by step solution

01

Analyze Reaction A

Identify the kinetic order of Reaction A. A half-life that is independent of the initial concentration indicates a first-order reaction. In first-order kinetics, the rate is directly proportional to the concentration of the reactant, and the half-life is constant regardless of the initial concentration.
02

Analyze Reaction B

Determine the kinetic order of Reaction B. A half-life that doubles when the initial concentration of the reactant doubles is characteristic of a second-order reaction. In second-order kinetics, the rate is proportional to the square of the concentration of the reactant, and thus the half-life is inversely proportional to the initial concentration.
03

Analyze Reaction C

Examine the kinetic order of Reaction C. A half-life that doubles when the initial concentration of the reactant is halved suggests a zero-order reaction. In zero-order kinetics, the rate is independent of the concentration of the reactant, and as the concentration decreases, the half-life increases.
04

Match Observations to Options

Compare the kinetic orders derived from observations with the options provided. Reaction A exhibits first-order kinetics, Reaction B exhibits second-order kinetics, and Reaction C exhibits zero-order kinetics.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

First-Order Reaction
In understanding chemical kinetics, a first-order reaction is fundamental to grasp. It's one where the rate at which the reaction occurs is directly proportional to the concentration of a single reactant. This means that as you double the amount of reactant, you double the reaction rate. A characteristic feature of a first-order reaction is its constant half-life, which is the time taken for half of the reactant to be converted into product.

A practical example is the decay of radioactive substances, where the half-life remains unchanged regardless of how much substance you start with. If given that the half-life of a reaction does not change with the initial concentration of reactant, we can infer that such a reaction is first-order, just as in Reaction A from the problem statement.
Second-Order Reaction
A second-order reaction is characterized by a reaction rate that is proportional to the square of the concentration of one reactant, or to the product of the concentrations of two reactants.

One of the interesting aspects of second-order reactions is that their half-life values are directly related to the initial concentration of the reactant: as the concentration increases, the half-life decreases. This inverse relationship is helpful for identifying second-order reactions in practice. If you observe that the half-life of a reaction doubles when the initial concentration doubles, as happens with Reaction B, you're likely dealing with a second-order reaction.

Second-order reactions are common in processes where two reactant molecules collide and react, such as the dimerization of alkenes under specific conditions.
Zero-Order Reaction
Moving on to the specifics of a zero-order reaction, this is a reaction where the rate is constant and unaffected by the concentration of the reactant. That's right; in zero-order kinetics, the reaction cruises at its own pace regardless of how much reactant is available.

Another peculiarity of zero-order reactions is their changing half-life: as the reactant concentration reduces, the half-life increases. This is because the reaction rates are no longer “throttled” by the reactant's concentration—it's as if the reaction is saying, 'I'll take my time, thank you very much.' Reaction C is a perfect example of zero-order kinetics, showcasing the increasing half-life with decreasing concentration.
Reaction Rate
The reaction rate is the speed at which a chemical reaction proceeds. It's the cornerstone of chemical kinetics, the field that unpacks the complexities of how reactions happen. The rate can be influenced by several factors, including reactant concentrations, temperature, and the presence of catalysts.

To put it in everyday terms, think of reaction rate like the speed of your car. Just as you can accelerate by pressing down on the gas pedal, you can increase the reaction rate by increasing the concentration of reactants or raising the temperature. The understanding of reaction rates is crucial, as it helps chemists control and optimize reactions for industrial processes, environmental modeling, and even pharmaceutical drug development.
Half-life of Reaction
Lastly, the half-life of a reaction is an informative concept that provides insights into the duration and progress of a chemical reaction. It is the period required for the concentration of a reactant to decrease by half its initial amount. In the context of different order reactions, half-life behaves differently.

For a first-order reaction, the half-life is a constant value, independent of the initial concentration. In a second-order reaction, the half-life is inversely proportional to the initial concentration, making it a variable that decreases with increasing concentration. In zero-order reactions, the half-life increases as the initial concentration decreases. Recognizing these patterns in half-life behavior is vital for chemists to predict how long a reactant will last under different conditions and to design reactions for desired outcomes.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The data shown here were collected for the first-order reaction: \(\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{O}(g)\) Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction. $$ \begin{array}{cc} \text { Temperature (K) } & \text { Rate Constant (1/s) } \\ 800 & 3.24 \times 10^{-5} \\ \hline 900 & 0.00214 \\ \hline 1000 & 0.0614 \\ \hline 1100 & 0.955 \\ \hline \end{array} $$

The rate constant \((k)\) for a reaction was measured as a function of temperature. A plot of In \(k\) versus \(1 / T\) (in \(\mathrm{K}\) ) is linear and has a slope of -7445 K. Calculate the activation energy for the reaction.

A reaction in which \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C}\) react to form products is first order in A, second order in B, and zero order in C. a. Write a rate law for the reaction. b. What is the overall order of the reaction? c. By what factor does the reaction rate change if [A] is doubled (and the other reactant concentrations are held constant)? d. By what factor does the reaction rate change if [B] is doubled (and the other reactant concentrations are held constant)? e. By what factor does the reaction rate change if [C] is doubled (and the other reactant concentrations are held constant)? f. By what factor does the reaction rate change if the concentrations of all three reactants are doubled?

The decomposition of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is first order in \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) and has a rate constant of \(1.42 \times 10^{-4} \mathrm{~s}^{-1}\) at a certain temperature. a. What is the half-life for this reaction? b. How long will it take for the concentration of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) to decrease to \(25 \%\) of its initial concentration? c. If the initial concentration of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is \(1.00 \mathrm{M}\), how long will it take for the concentration to decrease to \(0.78 \mathrm{M} ?\) d. If the initial concentration of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is \(0.150 \mathrm{M},\) what is the concentration of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) after \(2.00 \times 10^{2} \mathrm{~s}\) ? After \(5.00 \times 10^{2} \mathrm{~s} ?\)

Consider the reaction: $$ 8 \mathrm{H}_{2} \mathrm{~S}(g)+4 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{S}_{8}(g) $$ Complete the table. $$ \begin{array}{lllll} \Delta\left[\mathrm{H}_{2} S\right] / \Delta t & \Delta\left[\mathrm{O}_{2}\right] / \Delta t & \Delta\left[\mathrm{H}_{2} \mathrm{O}\right] / \Delta t & \Delta\left[\mathrm{S}_{8}\right] / \Delta t & \text { Rate } \\ -0.080 \mathrm{M} / \mathrm{s} & & & & \\ \hline \end{array} $$

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free