Chapter 13: Chemical Kinetics

Chemical Kinetics. Just the phrase may instill fear in your very heart and can cause you to suddenly see your somewhat short chemistry career flash by right in front of your eyes. Oh, the good old memories with your pals Sodium and Nitrogen... all spent in vain. I know the feeling. But don't worry! This page is designed to help you "get" chemical kinetics, not confuse you. Think of this as an easy-swallow pill; hey, if you can't swallow pills, that's okay too, this can be viewed as yummy flavored cough syrup. But enough of me rambling on...

First, let's start with some basic definitions. I always find it easy to start with square one.

Chemical Kinetics- DEATH! Just kidding. This isn't nuclear chemistry, nor is it organic chemistry. So, chemical kinetics can be defined as the area of chemistry that concentrates on the rates in which reactions occur.

Reaction Rate- The change of the concentration of a reactant or product with time. Because it's pretty much a ratio of change of concentration vs. time, it is expressed usually in molarity over seconds, or M/S.

See? Two measly definitions so far. Not bad. So now that you know what the terms 'chemical kinetics' and 'reaction rate' mean, its time to step it up a notch. A squeaky little voice in the back of your head is probably asking you... "why is this important in the study of chemistry?" or the good old, "how does this apply to the actual world?" Usually these questions are accompanied with a good, long eye roll. Well, I'm here to tell you why.

The Importance of Chemical Kinetics
Because all chemical reactions have different rates, it easily applied to the real life world. And you live in AMERICA!!! That itself should ring a bell. "The land of the free" is one of the biggest producers of consumer goods. We pollute and kill things, and build factories like there's no tomorrow. We bask in the glory of being the number one producer in garbage; we also have to work hard to make it seem like we undo some of the bad things we do to the environment... SO... we use chemistry to our advantage and use CHEMICAL KINETICS for pollution control, food processing, drug design, industrial works, and other neat-o things!

Now, let's review some chemistry basics so that you can fully comprehend all this "chemical kinetics stuff." You already know that the basic equation for most/all chemical reactions is represented in the equation:

REACTANTS à PRODUCTS, or, A àB Since the decrease in the molecules of reactant A would lead to an increase in product B, the reaction rate expressing change in the concentration vs. time for each is expressed by:

...where [A] and [B] stand for concentration in molarity and t stands for time. The reason why the rate of reactant of A is expressed in negative form can be argued because the ractant A decreases as in time while the product B increases in time. As a study tip, everytime you think of rate of reactions (for most general purposes) think A= DOWN, B=UP.

Now, you're probably wondering how these crazy scientists figured this out, or even worse, obtained the actual rate itself. Well, although they seem like magicians pulling bunnies out of their hats, scientists actually calculate the rates by using spectrocopic means during real live chemical experiments. When our friends the ions are involved, the change in concentrations can be detected by an electrical conductance measurement. At the same time, when gases come into the picture, scientists use pressure measurements instead of the conductance/spectroscopic methods.

Reaction Rates + Stoichiometry
Not all reactions will be so point blank... most of the equations you'll see in you're chemistry class are much more advanced than something like Na+ + Cl- -> NaCl. So! We must prepare you for battle! One things for sure, you must heed my warnings while writing your reaction rates...
... AN EXAMPLE: The generic equation of a one to one ratio as seen before was symbolized as A->B. However, what if the reaction was derived from the equation where 2A -> B? That should by now raise a red flag in the sky to signify that two moles of A disappear in each mole of B that forms... WHICH ALSO MEANS that the rate of the disappearence of rectant A occurs twice as fast as the rate of the appearence of product B. Thus, for a rate like 2A -> B, the rate equations would be shown as:


Now you know how to write the equation for the rates expressing change in concentration over time, its time to bring in the big guns. I'm so serious... you're in the big league now! Since we reviewed the basics and you met the generic family (mom, dad, aunt sally), it's time to meet THE RATE LAW. I know, it doesnt sound so intimidating... the rate law sounds more like some legislation passed in Congress to kill more fish or something... BUT ITS NOT. Its legit. If you haven't taken calc yet, you need not to heed how to derive the different rate laws. However, I feel as though if you've already met the little devil calculus, pass to go and collect your two hundred dollars. In other words, bite the bullet and take it in. It will help you better understand how such funky equations were concieved.


The Rate Law
UH-OH spaghetti-os. It's showtime. Basically, the rate law can be defined as the law which expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to some power. Thus, the general rate law can be expressed by the equation:

...where z and y are numbers that are obtained only through experimental means. Understand that unlike the friendly equation aA+ bB -> cC + dD, the exponents x and y are not equal and therefore do not substitute for the stoichiometric coefficients a and b. [A] and [B] still stand for the concentrations in molarity. When x and y are added together, the sum is equaled to the overall reaction order.
The definition of reaction order could be stated as: the sume of the powers to which all reactant concentrations appearing in the rate law are raised. In effect, using the general rate law equation above, since x + y = overall reaction rate, x = reaction rate of A and y = reaction rate of B.

How to find the 'Initial Rate' of an equation
Finding the initial rate law of an equation isn't like playing hide and seek, nor is it trying to kill something by taking a stab in the dark. The only reason why its considered somewhat confusing or complicated is because it deals with equations that differ from the norm. FOR EXAMPLE, as I stated above, the most general equation used for expressing any given chemical equation can be expressed by: reactants yield products. However, some equations follow the reverse form where the products yield the reactants. This can give false answers and false results if inserted into the rate law expression. To avoid this disasterly and 'Titantic' like tragedy, we use tables (given) to determine which numbers to use. Using the table can also give information used to find the wonderful constant k. BINGO!

Hard times call for Generic Directions...
1. MAKE SURE THERE IS A CHART! This chart must depict the rate data for a specific reaction between two plus substances... or else this will be the end of you. I kid you not.
2. If its an extremely lame word problem or is just cheap and doesn't give you an balances equation, FIGURE IT OUT AND WRITE IT DOWN!
3. Now, create a skeleton of the rate law equation.
4. Find the constant, k
5. Use the chart to figure out the orders.
6. Plug in all the values to find the rate!


F2_CLO2.JPGIn this particular example, the equation is:
Skeleton of rate law: rate = k[F2][ClO2]

Calculate the constant k:
k = rate/[F2][ClO2]
k = 1.2 x 10-3/
(0.10 M)(0.10 M)
= 1.2/ M∙s

Now... look back at the chart. When a substance stays the same in molarity, and the third colomn (the initial rate) changes, we find the singular rate order by dividing the larger numbers by the smaller number. As a notable example, using the chart, F2 stays the same in molarity in the first two experiments, while the initial rate jumps from (1.2 x 10^-4) to (4.8 x 10^-3). When you divide (4.8 x 10^-3) by (1.2 x 10^-4), the quotient is 4. This makes the rate order of F2 two. Right now, you may be thinking, "how the heck does the quotient of 2 signify a first order reaction??" or even... "what is a first order reaction?" For simplicity, for now I'm just going to make you remember that when you get a quotient of 1, the order of the substance is zero. When you get a quotient of 2, as we did above, the order of the substance is one. Finally, when you get a quotient of 4, the order of the substance is two. THAT'S IT!

So now that we found the constant, or konstant for hilarity purposes, we can plug in the orders and find the rate!
rate = (1.2/ Ms) [0.10]^2[0.10]^1
rate = .0012

Relation Between Reactant Concentration and Time
Before, I spoke of a nebulous term, "first/second/zero order."Don't panic. Let's define them now!
Zero-Order Reactions- Reactions whose rates depend on the reactant concentrations raised to the zero power
First-Order Reactions- Reactions whose rates depend on the reactant concentrations raised to the first power
the equation for the rate law for first order reactions is arate = negative delta A/ delta t. This can be explained and derived from by using the above chart.
Second-Order Reactions- Reactions whose rates depend on the concentration of one reactant raised to the second power, or on the concentrations of two different reactants
To better understand these graphs as well as the definitions, the introduction of the basic equations as well as seeing how each is equation is derived is essencial (in my opinion, of course). The following PDF file explains how the equations for each order can be derived. It isn't essential to fully understand the calculus aspect, the thing that most matters is the last part of the equation. It helps to understand how each equation fits into the form y = mx + b. Surely you know what that is. I won't insult your intelligence.

Now, the last problem asked us to figure out half-lifes. That hasn't been introduced to you yet! But dont you worry... this next explaination will clarify everything. Have faith.



This lab has a worksheet with the written directions and questions that should be answered for a bettter overall understanding...

Go to the website:
Read through all the directions and explainations
You will see the first screen which looks like this:
Then attempt the second part which looks like this:

Part Two- Differential Rate Law
Go to the website:
Read through all the directions and explainations
View the graphs above the virtual simulation, then go to the screen:

Part Three- Integrated Rate Law
Go to the website:
Read through all the directions and explainations
View the different graphs provided
Follow the directions and use the simulations as the screen below:

Collision Theory of Chemcial Kinetics
rate = number of collisions / s
So to express a rate law, we would use the equation rate = k [A][B]

Rules of the Collision Theory
1. The molecules of a reaction must hit eachother (to make energy of course)
2. The molecules must hit with enough energy (when there is too little energy, nothing happens)
3. The molecules must hit in the right orientation

...or think about it like beating up your friend:
1. You must hit your friend to do some damage (black eye, bloody nose, knuckle sandwich..etc?)
2. You must hit your friend with enough gusto or you'll be considered a weenie (I would say "hit like a girl," but hey, thats sexist...)
3. You must hit your friend in the sweet spots, or else they'll just brush it off like its no biggie

What are the Effects?
Besides risking doing some time in the big bad jailhouse (for beating up your friend)... when molecules collide with the right amount of force and the right spot, the effects include changes in temperature, concentration, and catalysts.

activation energy (Ea) - the minimum amount of energy required to initiate a chemical reaction
activated complex- what molecules form when they collide
transition state- a temporary species formed by the reactant molecules as a result of the collision before they form the product

The Arhhenius Equation

Reaction Mechanics

elementary steps- (elementary reactions) a series of simple reactions that represent the progress of the overall reaction at the molecular level
reaction mechanism- the sequence of elementary steps thatleads to product formation
intermediates- species that appear in the mechanism of the reaction but not in the overall balanced equation
molecularity of a reaction- the number of molecules reacting in an elementary step
bimolecular reaction- an elementary step that involves two molecules
termolecular reaction- the reaction that involves the participation of three molecules in one elementary step (rare)
rate determining step- the slowest step in the sequence leading to product formation

The two requirements that elementary steps must satisfy:
1) The sum of the elementary steps must give the overlal balanced equation for the reaction
2) The rate determining step should predict the same rate law as is determined experimentally


What do Catalysts do?

Big Surprise. This is probably a review. Catalysts speed up reactions by lowering the activation energy. It cannot be consumed during reactions and there are two types. Bet you didn't know that!
1. Heterogeneous Catalysts: Catalysts that change into different states during a reaction (such as solid to gas)
2. Homogeneous Catalysts: Catalysts that retain the same state during a reaction (such as liquid to liquid)

Super Websites About Chemical Kinetics for Further Help, Study, + Notes:

Some resources:
Chemistry, 8/e----
Raymond Chang, Williams College