/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 82 What are the units of the rate c... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

What are the units of the rate constant for a thirdorder reaction?

Short Answer

Expert verified
The units of the rate constant for a third order reaction are (liters squared per mole squared) per time.

Step by step solution

01

Understand the Order of Reaction

For a chemical reaction, the rate law is given by: Rate = k[A]^m[B]^n where A and B are reactants, m and n are orders with respect to reactants A and B, and k is the rate constant. The overall order of the reaction is the sum of the individual orders, that is m + n.
02

Relate Order of Reaction to Units of Rate Constant

For a third order reaction, the rate of the reaction is directly proportional to the cube of the concentration of the reactants (total order = 3). The overall reaction rate is given by: Rate = k[A]^3 Considering the units: - Rate of reaction is typically in moles / liter / time - Concentration [A] is typically in moles / liter Therefore, to balance the units on both sides of the equation, k, the rate constant, must be in (liter^2 / mole^2) / time.
03

State the Units of Rate Constant for a Third Order Reaction

In conclusion, for a third order reaction, the units of the rate constant (k) are (liters squared per mole squared) per time. This is because the rate constant must compensate for the units of rate concentration to the power of the reaction order in the rate law expression.

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 91Ó°ÊÓ!

Key Concepts

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

Third Order Reaction
A third order reaction is a chemical reaction where the overall order of the reaction is three. This type of reaction typically involves either:
  • Three molecules of a single reactant coming together in a single step or,
  • One or more molecules of different reactants that collectively result in a third-order rate law.
In a third order reaction, the rate of the reaction depends on the concentration of the reactants raised to a power such that the exponent adds up to three. For example, it could be \[ ext{Rate} = k[A]^3 \ \] or \[ ext{Rate} = k[A][B]^2 \] where the sum of the exponents is three. Here, \( k \) is the rate constant.
Third order reactions are less common than first and second order reactions due to the low probability of three molecules colliding with the proper orientation and sufficient energy to result in a reaction.
Rate Law
The rate law of a chemical reaction is an equation that links the rate of a reaction to the concentration of reactants. It shows how changes in the amounts of reactants can affect the speed of the reaction. Here's the basic form of the rate law:
  • Rate = k[A]^m[B]^n
In the rate law, \( k \) represents the rate constant, \([A]\) and \([B]\) are concentrations of reactants, and \( m \) and \( n \) are the order of the reaction with respect to each reactant.
Each reaction has its own rate law, which must be determined experimentally due to its dependence on the specific mechanism of the reaction.
The rate law helps chemists understand the dynamics of the reaction and can provide insight into the mechanism of the reaction itself.
Chemical Kinetics
Chemical kinetics is the study of the rates of chemical processes and the factors that affect these rates. It involves measuring how quickly reactions occur and understanding the elements that influence these changes.
Factors in chemical kinetics include:
  • The concentration of reactants: Higher concentrations often increase the rate of reaction.
  • Temperature: An increase in temperature generally increases reaction rates.
  • Catalysts: Substances that increase the rate of reaction without being consumed.
  • The surface area of solid reactants: Greater surface area can lead to faster reaction rates.
The knowledge of chemical kinetics is essential for understanding how reactions progress, which is crucial in fields ranging from pharmaceutical development to environmental science.
Reaction kinetics gives insight into optimizing reaction conditions for industrial applications, ensuring processes run safely and efficiently.
Reaction Order
Reaction order is a key concept in chemical kinetics that indicates how the rate of reaction is affected by the concentration of one or more reactants. It is derived from the exponents in the rate law equation.
  • The order of a reaction can be zero, first, second, or even higher, depending on how many concentration terms are involved.
  • Order is found by adding together the exponents of the concentration terms in the rate law.
For example, in a rate law such as \( ext{Rate} = k[A]^m[B]^n \), the overall order of the reaction is \( m+n \). Each order provides unique insights into the mechanics of a reaction:
  • First order reactions depend linearly on one reactant.
  • Second order reactions may depend on two different reactants or be second order in one reactant.
  • Third order, as explained earlier, can involve three molecules simultaneously.
Understanding reaction order aids in predicting the behavior of reactions in different conditions, such as how long it will take for a certain amount of reactant to be used up.

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

Consider the second-order reaction $$ \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}(g)+\mathrm{Cl}(g) $$ Given that the frequency factor and activation energy for the reaction are \(4.0 \times 10^{9} / M \cdot \mathrm{s}\) and \(85 \mathrm{~kJ} / \mathrm{mol}\), respectively, calculate the rate constant at \(500^{\circ} \mathrm{C}\).

Reactions can be classified as unimolecular, bimolecular, and so on. Why are there no zeromolecular reactions? Explain why termolecular reactions are rare.

Define activation energy. What role does activation energy play in chemical kinetics?

Polyethylene is used in many items, including water pipes, bottles, electrical insulation, toys, and mailer envelopes. It is a polymer, a molecule with a very high molar mass made by joining many ethylene molecules together. (Ethylene is the basic unit, or monomer for polyethylene.) The initiation step is $$ \mathrm{R}_{2} \stackrel{k_{1}}{\longrightarrow} 2 \mathrm{R} \cdot \quad \text { initiation } $$ The \(\mathrm{R} \cdot\) species (called a radical) reacts with an ethylene molecule (M) to generate another radical $$ \mathrm{R} \cdot+\mathrm{M} \longrightarrow \mathrm{M}_{1} $$ Reaction of \(\mathrm{M}_{1} \cdot\) with another monomer leads to the growth or propagation of the polymer chain $$ \mathrm{M}_{1} \cdot+\mathrm{M} \stackrel{k_{\mathrm{p}}}{\longrightarrow} M_{2} \cdot \quad \text { propagation } $$ This step can be repeated with hundreds of monomer units. The propagation terminates when two radicals combine \(\mathrm{M}^{\prime}+\mathrm{M}^{\prime \prime} \cdot \stackrel{k_{1}}{\longrightarrow} \mathrm{M}^{\prime}-\mathrm{M}^{\prime \prime} \quad\) termination The initiator frequently used in the polymerization of ethylene is benzoyl peroxide \(\left[\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}\right)_{2}\right]:\) $$ \left[\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}\right)_{2}\right] \longrightarrow 2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO} $$ This is a first-order reaction. The half-life of benzoyl peroxide at \(100^{\circ} \mathrm{C}\) is 19.8 min. (a) Calculate the rate constant (in \(\min ^{-1}\) ) of the reaction. (b) If the half-life of benzoyl peroxide is \(7.30 \mathrm{~h},\) or \(438 \mathrm{~min},\) at \(70^{\circ} \mathrm{C},\) what is the activation energy (in \(\mathrm{kJ} / \mathrm{mol}\) ) for the decomposition of benzoyl peroxide? (c) Write the rate laws for the elementary steps in the above polymerization process, and identify the reactant, product, and intermediates. (d) What condition would favor the growth of long, highmolar-mass polyethylenes?

Strontium-90, a radioactive isotope, is a major product of an atomic bomb explosion. It has a half-life of 28.1 yr. (a) Calculate the first-order rate constant for the nuclear decay. (b) Calculate the fraction of \({ }^{90} \mathrm{Sr}\) that remains after 10 half-lives. (c) Calculate the number of years required for 99.0 percent of \({ }^{90} \mathrm{Sr}\) to disappear.

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.