Unit 5 Beta

Kinetics: the one-page sheet

5.1 Reaction Rates

A reaction rate is the change in concentration of a reactant or product per unit time, in M/s. Rates of different substances are linked by their coefficients. Concentration, temperature and surface area change the rate, while the limiting reactant sets how much product forms.

A reaction rate is the change in concentration per unit time, in M/s. Reactant rates carry a minus sign so they come out positive.
Average rate is the slope between two points; instantaneous rate is the slope of the tangent at one time; initial rate is the tangent at t = 0.
Divide each substance's rate by its coefficient to get one rate for the reaction.
Rate is how fast product forms. The amount of product is set by the limiting reactant.
Higher concentration, higher temperature and more surface area make a reaction faster.

the reactant concentration falls and the product concentration rises fewer react each second, so the curve flattens and the rate falls the rates of different substances are linked by their coefficients the reaction goes faster, but the amount of product is still set by the limiting reactant

reaction rate: How fast the concentration of a reactant or product changes with time, usually in M/s. The average rate is measured between two times, the instantaneous rate at one moment, and the initial rate at the start.

5.2 Introduction to Rate Law

A rate law, rate = k[A]^m[B]^n, gives how the rate depends on each reactant concentration. The orders come from initial-rate data by changing one concentration at a time. The rate constant k is fixed at a given temperature, and its units depend on the overall order.

A rate law has the form rate = k[A]^m[B]ⁿ. The orders m and n come from experiment, not from the coefficients.
Order 0: rate unchanged when [A] changes. Order 1: rate changes by the same factor. Order 2: rate changes by the factor squared.
Method of initial rates: compare two trials where only one concentration changes.
k depends on the reaction and the temperature, not on concentration. Its units are M/s divided by M raised to the overall order.

any change in the initial rate is caused by that reactant alone comparing the two factors gives the order for that reactant any one trial gives the rate constant k, whose units follow from the overall order the rate law predicts the rate for any new set of concentrations

rate law: An equation, found by experiment, that gives the rate of a reaction in terms of reactant concentrations: rate = k[A]^m[B]^n.
rate constant: The constant k in a rate law. It is fixed for a reaction at a given temperature, rises with temperature, and has units that depend on the overall order.
reaction order: The exponent on a concentration in a rate law (0, 1 or 2 in this course). The overall order is the sum of the exponents.
method of initial rates: Finding the orders of a rate law by comparing the initial rates of trials in which only one starting concentration changes.

5.3 Concentration Changes Over Time

Integrated rate laws link concentration and time. The plot that is linear identifies the order: [A] vs t for zero order, ln[A] vs t for first order, 1/[A] vs t for second order, and its slope gives k. A first-order reaction has a constant half-life, t½ = 0.693/k.

Zero order: [A] vs t is linear (slope −k). First order: ln[A] vs t is linear (slope −k). Second order: 1/[A] vs t is linear (slope +k).
Justify an order by naming the plot that is linear.
First-order half-life: t½ = 0.693/k, independent of concentration. Radioactive decay is first order.
Integrated laws use ln, not log.

each order makes a different plot of the data come out straight naming that plot identifies the order, and its slope gives k the half-life is constant: t½ = 0.693/k you can predict the concentration at any time or the time to reach any concentration

integrated rate law: An equation linking a reactant concentration to time, such as ln[A]t − ln[A]0 = −kt for a first-order reaction.
linear plot: The graph of concentration data that comes out as a straight line for a given order: [A] vs t (zero), ln[A] vs t (first) or 1/[A] vs t (second). Its slope gives k.
half-life: The time for a reactant concentration to fall to half its value. For a first-order reaction it is constant: t½ = 0.693/k.

5.4 Elementary Reactions

An elementary reaction happens in a single event, so its rate law follows from its coefficients and its molecularity is the number of particles in that event. Bimolecular steps are the most common and termolecular steps are rare. Overall reactions usually happen in several steps, so their rate laws must be measured.

An elementary reaction is one event: a single collision or one particle breaking apart.
The rate law of an elementary step uses its coefficients as orders: 2 A + B → products has rate = k[A]²[B].
Molecularity: unimolecular (1), bimolecular (2, most common), termolecular (3, rare).
Only elementary steps follow this rule. Overall rate laws are measured.

its rate depends on how often those exact particles meet each particle in the step contributes one power of its concentration you can write its rate law without an experiment its rate law must still come from data

elementary reaction: A reaction that happens in a single event at the particle level: one collision, or one particle breaking apart. Its rate law follows from its coefficients.
molecularity: The number of reactant particles that come together in an elementary step: unimolecular (one), bimolecular (two) or termolecular (three, rare).

5.5 Collision Model

A reaction happens when particles collide with at least the activation energy and a suitable orientation. Raising the temperature raises the fraction of collisions with enough energy far more than it raises the collision frequency, so the rate and the rate constant increase while the activation energy stays the same.

A reaction happens through effective collisions: enough energy (at least E_a) and the right orientation.
Most collisions do not react, because they lack the energy, the orientation, or both.
Higher temperature: a little more collision frequency, and a much larger fraction of collisions above E_a. E_a itself does not change.
At the same temperature, a smaller E_a means a faster reaction and a larger k.

a reaction is possible only where they meet a collision needs at least the activation energy a collision also needs a suitable orientation a larger fraction of collisions clears the same barrier, so the rate and k rise

collision model: The idea that particles react only when they collide with at least the activation energy and a suitable orientation; such collisions are effective collisions.
activation energy: The minimum energy a collision must have for the colliding particles to react. It is set by the reaction pathway, not by the temperature.

5.6 Reaction Energy Profile

An energy profile shows potential energy along the reaction coordinate. The activation energy is the rise from the reactants to the transition state, and the energy change is products minus reactants. At the same temperature, a higher barrier means a smaller rate constant, whatever the overall energy change.

An energy profile plots potential energy against reaction progress, from reactants through the transition state to products.
E_a = E(transition state) − E(reactants). Energy change = E(products) − E(reactants).
Energy change = E_a(forward) − E_a(reverse).
A higher barrier means a smaller k and a slower reaction at the same temperature. The overall energy change does not set the rate.

potential energy rises to a peak, the transition state a higher peak means fewer collisions succeed and a smaller k products minus reactants gives the energy released or absorbed the difference between their barriers equals the energy change

reaction energy profile: A graph of the potential energy of reacting particles against reaction progress (the reaction coordinate), from reactants through the transition state to products.
transition state: The highest-energy arrangement of atoms along a reaction path, with bonds partly broken and partly formed. It cannot be isolated.

5.7 Introduction to Reaction Mechanisms

A reaction mechanism is a sequence of elementary steps that adds up to the overall balanced equation. Intermediates are made in one step and used in a later one, so they cancel from the sum. A mechanism must sum correctly and use reasonable steps, and it is a proposed explanation, consistent with the evidence rather than proven.

A reaction mechanism is a series of elementary steps that adds up to the overall equation.
An intermediate is made in one step and used in a later step; it does not appear in the overall equation.
Add the steps and cancel species that appear on both sides to check a mechanism.
A mechanism that passes the tests is consistent with the evidence, not proven.

most reactions happen in a series of one- and two-particle elementary steps they cancel when the steps are added: they are intermediates this sum test rules out some proposed mechanisms a mechanism is only consistent with the evidence, never proved by it

reaction mechanism: The series of elementary steps by which a reaction happens. The steps must add up to the overall balanced equation.
reaction intermediate: A species made in one step of a mechanism and used up in a later step. It does not appear in the overall equation.

5.8 Reaction Mechanism and Rate Law

The slowest step of a mechanism is the rate-determining step. When the first step is slow, the overall rate law is that step's rate law, so reactants used only in later fast steps do not appear. A mechanism is consistent with experiment when the rate law it predicts matches the measured rate law.

The rate-determining step is the slowest step; the overall rate cannot be faster than it.
If the first step is slow, the overall rate law is the rate law of that step.
Reactants that enter only after the slow step do not appear in the rate law.
A mechanism is consistent with data if its predicted rate law matches the measured one. It is never proven.

the reaction cannot run faster than its slowest step the overall rate law is that step's rate law, written from its coefficients they do not appear in the rate law (zero order) a mismatch rules a mechanism out; a match makes it consistent with the data

rate-determining step: The slowest elementary step in a mechanism. It limits the overall rate, so the overall rate law follows from it.

5.9 Pre-Equilibrium Approximation

When a fast reversible step comes before the slow step, its forward and reverse rates are equal. That equality gives the intermediate's concentration in terms of reactants, which is substituted into the slow step's rate law. The result contains only reactants, with a combined rate constant, and can be compared with the measured rate law.

A reversible reaction step runs forward and in reverse (⇌), each with its own rate constant.
When a fast reversible step comes before a slow step, set its forward rate equal to its reverse rate (pre-equilibrium).
Solve for the intermediate, substitute into the slow step's rate law, and combine constants: k = k₂k₁/k₋₁.
A final rate law contains no intermediates.

the fast step runs back and forth many times and stays balanced k₁[reactants] = k₋₁[intermediate] gives the intermediate in terms of reactants substituting removes it, leaving only reactant concentrations the predicted rate law can be compared with the measured one

reversible reaction: A reaction or step that runs in both directions, written with ⇌. The forward reaction turns reactants into products; the reverse reaction turns products back into reactants.
pre-equilibrium: The approximation that a fast reversible step before the slow step has equal forward and reverse rates, used to express an intermediate's concentration in terms of reactants.

5.10 Multistep Reaction Energy Profile

A multistep energy profile has one peak, a transition state, for each elementary step, with intermediates in the valleys between them. Each step's activation energy is measured from its own starting level, and the step with the largest barrier is the rate-determining step. The overall energy change is products minus reactants.

A multistep energy profile has one peak per elementary step; valleys between peaks are intermediates.
A step's E_a is its peak minus the level it starts from.
The step with the largest E_a is the rate-determining step; it need not be the first.
The overall energy change is products minus reactants, whatever happens in between.

a mechanism with n steps has n peaks on its profile it sits in a valley between neighboring peaks its barrier is measured from that level, not from the reactants it is the slow, rate-determining step

multistep energy profile: The energy profile of a reaction with several elementary steps: one peak (transition state) per step, with intermediates in the valleys between peaks.

5.11 Catalysis

A catalyst speeds a reaction by providing a different mechanism with lower activation energies. It is consumed in one step and regenerated in a later one, unlike an intermediate, which is made and then used. A catalyst leaves the overall energy change and the final amount of product unchanged.

A catalyst speeds a reaction by providing a new mechanism with lower barriers. It is used in one step and remade in a later step.
Catalyst: used, then remade. Intermediate: made, then used.
A catalyst does not change the overall energy change or the final amount of product, and it speeds the forward and reverse reactions alike.
Kinds: homogeneous, heterogeneous (surface), acid-base and enzymes.

the reaction goes by a different set of elementary steps more collisions succeed at the same temperature, so the rate rises it is not used up and cancels from the overall equation the overall energy change and the final amount of product stay the same

catalyst: A substance that speeds up a reaction by providing a mechanism with lower activation energies. It is used in one step and regenerated in a later one, so it is not consumed overall.