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Chemistry: The Collision Model

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About this Lesson

  • Type: Video Tutorial
  • Length: 12:08
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 129 MB
  • Posted: 07/14/2009

This lesson is part of the following series:

Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Chemical Kinetics (18 lessons, $25.74)
Chemistry: Collision Model & Arrhenius Equation (3 lessons, $4.95)

This lesson was selected from a broader, comprehensive course, Chemistry, taught by Professor Harman, Professor Yee, and Professor Sammakia. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/chemistry. The full course covers atoms, molecules and ions, stoichiometry, reactions in aqueous solutions, gases, thermochemistry, Modern Atomic Theory, electron configurations, periodicity, chemical bonding, molecular geometry, bonding theory, oxidation-reduction reactions, condensed phases, solution properties, kinetics, acids and bases, organic reactions, thermodynamics, nuclear chemistry, metals, nonmetals, biochemistry, organic chemistry, and more.

Dean Harman is a professor of chemistry at the University of Virginia, where he has been honored with several teaching awards. He heads Harman Research Group, which specializes in the novel organic transformations made possible by electron-rich metal centers such as Os(II), RE(I), AND W(0). He holds a Ph.D. from Stanford University.

Gordon Yee is an associate professor of chemistry at Virginia Tech in Blacksburg, VA. He received his Ph.D. from Stanford University and completed postdoctoral work at DuPont. A widely published author, Professor Yee studies molecule-based magnetism.

Tarek Sammakia is a Professor of Chemistry at the University of Colorado at Boulder where he teaches organic chemistry to undergraduate and graduate students. He received his Ph.D. from Yale University and carried out postdoctoral research at Harvard University. He has received several national awards for his work in synthetic and mechanistic organic chemistry.

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Thinkwell
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Everything we've said up until now regarding kinetics has been macroscopic. What's going on, on a level that we can actually measure in the laboratory? We measure concentrations as a function of time and things like that. Now what we want to do is connect what is going on in a macroscopic laboratory level with what is really going on, on an atomic molecular level.
The first thing that we are going to do is consider something called collision theory. Collision theory says this: Chemical reactions occur because atoms or molecules smash into each other. When they smash into each other it can lead to products. What we are going to do is develop that idea a little more quantitatively. What we are going to see is that we can actually explain a macroscopically observed rate law expression.
When we are talking about two things colliding with each other in collision theory, it is almost always going to be two things that collide. The reason is that when we talk about things colliding, we mean that they actually have to collide simultaneously. It turns out to be extremely unlikely for three things to collide simultaneously. When two things smash, there you go. If you think about when you are shooting pool, you and two friends each hit a ball toward the center of the table. Even if you all had perfect aim, the likelihood that all three balls would hit each other at exactly the same moment is infinitesimally small. It's not zero, but it tends to be really, really small. It is much less likely for three balls to come together simultaneously than it is for two balls to collide into each other. When we talk about collisional theory, we are always really talking about two things smashing into each other not three things or more. That idea is going to become much more important later on, but for right now, try to keep that in mind.
For bimolecular reactions, the rate is equal to the rate constant times the concentration of the first reactant times the concentration of the second reactant. If you think back to the analogy of the Junior High School dance, which is what we are going to use over and over in this lecture. I said that the rate of production of couples dancing on the dance floor at the Junior High School dance is proportional to the number of boys and the number of girls or also the product of the number of boys and the number of girls. That idea is embodied in this expression of rate.
In collision theory, we are going to assume that the rate of reaction is equal to the collision rate times the fraction of collisions that lead to products. In other words, going back to the analogy of the Junior High School dance, it is going to depend on how often boys are asking girls to dance or girls are asking boys to dance times the fraction of those invitations to dance that they are accepting. That is going to affect the rate of production of dancing couples on the dance floor.
If none of the girls feels like dancing, then the rate of production of dancing couples is going to go to zero. If none of the boys ever ask any of the girls, then the rate of production of dancing couples is also going to be zero. At least in the limit of extremes, this idea makes sense.
Now let's look at the issues that affect collision rate and fractions of collisions that lead to products. The first one I want to focus on is the fraction of collisions that leads to products. One of the issues that affects the fraction of collisions that leads to products is the fact that when you have a reaction there is something called an activation barrier to leading to products. One of the analogies is if you are a couch potato, you are sitting and you are watching football. If you sit in a very soft couch and you are really down there in those cushions then there is a large activation barrier. In other words, it takes a lot of energy to get up and get out of the couch to go and get another beer and a sack of chips. Now, there might be really large driving force. You might really want another beer and a sack of chips. However, because you are sitting in a really soft sofa where you are nestled down in there, you have to put a lot of energy to get yourself out of the sofa in order to get to the refrigerator. Conversely, if you are sitting on a hard chair, it might take less energy or there is smaller activation energy to get up and go and get your refreshments.
That idea in chemistry says that here we have A and some other molecule BC, and ultimately the product is AB + C. So, some sort of bimolecular reaction where we have one molecule and another molecule and there is some sort of transfer to get AB + C.
We have already talked about the fact that the enthalpy changed. This axis is energy and this axis is what we call the reaction coordinate. We have already talked about the idea that this is the enthalpy change. In other words, this is an exothermic reaction. There might be a large driving force for this reaction to occur. What makes the reaction relatively fast or slow is the size of this hump or the barrier to get from reactants to products. We call the energy difference between where reactants start and the top here the activation energy or E[a] for the forward reaction because we are talking about going for the forward reaction. We call this A...B...C, the activated complex. What it consists of is something that is in between A + BC and AB + C, where we have started to form the bond between A and B and we've started to break the bond between B and C. It turns out that is endothermic with respect to reactants and endothermic with respect to products.
In other words, to get to a place where we are starting to break these bonds here and starting to make these bonds, you actually have to put some energy in. That energy corresponds to the activation energy. The more you have to put in to get to the activated complex, the slower the reaction is going to be because you have to get up a higher hill.
Where does this energy come from? It comes from the kinetic energy of the molecules that are reacting. In other words, A and BC are moving toward each other and boom, they sort of come to a stop or at least some of their kinetic energy gets converted into potential energy. That potential energy allows them to ramp up this hill. If everything is moving slowly and lethargically then the probability that any collision between an A and a BC is going to go all the way up to give this activated complex as low. In other words, things moving slowly are less likely to have enough energy to get all the way up the hill. That idea is embodied in the expression, f, which is the fraction of collisions with enough energy now to react, is equal to the exponential of where E[a] is the activation energy, R is the gas constant expressed in joules per mole Kelvin, and T is the temperature. Qualitatively, what this says is at higher temperatures f is larger. The higher the temperature is the more the particles are going to be moving with enough energy to get up over the hill. So, f has a really strong temperature dependence, and to give you some idea of how small this exponential can be -- if the activation energy is 75 kilo joules per mole, and at room temperature RT, plug in, R 8.31 joules per mole Kelvin. T is temperature in Kelvin, so it has RT has a value of 2.5 kilo joules per mole, so the exponential of e is 7 10^-14, which means only 7 out of every 100 trillion collisions gives rise to a successful product, gives rise to a collision that gets over the hump. Only 1 of every 100 trillion collisions has enough energy to get over the top and down.
If this were your probability of getting a girl to dance with you, it would not be too good. Fortunately, this is just the probability that two molecules have enough energy when they collide to get over the hump.
This is probably relatively meaningless to you, but it turns out that there is a rule of thumb. The rule of thumb is that for a lot of everyday reactions at room temperature, increasing the temperature of the reaction by 10 degrees Celsius doubles the rate. Conversely, decreasing it by 10 Kelvins or 10 degrees Celsius halves the rate. That turns out to be important and we'll talk about that more when we are talking about cooking and stuff like that.
There is another issue that affects the probability that a collision is going to be successful. That is p the steric factor. In other words, not all collisions are of the right orientation. The analogy would be if you go to a dance, a junior high school dance, and you have enough charisma and enough gumption to go up and ask a girl to dance. That would be the f part. Suppose you are talking to a girl, but you are talking to her back, she doesn't even hear you. You are standing there and you are pouring your heart out asking her to dance, but she doesn't see you because you are talking to her back. Your orientation is incorrect. You have enough propensity to get up out of your chair and ask her to dance, but you are just not pulling it off. What happens is the number of collisions that are successful is compromised by this amount, p, the steric factor, and it varies between 0 and 1. In other words, none of the reactions are oriented correctly versus all of the reactions are oriented correctly.
Here's an example. Here is the reaction of ozone and nitric oxide going to nitrogen dioxide and 0[2], and the blues are nitrogen and the reds are the oxygens. The top one is oriented correctly, so these two things collide. What we are trying to do is transfer an oxygen from here to this nitrogen to make NO[2]. We are going to break this bond and form this bond. You can see that if it collides on the wrong end of the nitric oxide molecule, then what happens is you are not going to lead to products. That is going to compromise your probability of a successful reaction.
The third piece is that the collision rate is going to depend on the concentration of A, the concentration of B, and then this factor Z that makes all the units turn out and that also reflects the speeds of the molecules. In other words, how often these things collide. If you think back to the kinetic molecular theory of gases, the collision rate with the wall only depended on the concentration of gases. Now we're talking about the collisions between A's and B's, so it is going to depend on both the concentration of A and the concentration of B. It turns out that this thing, which is how fast the molecules move, how fast they move as a function of temperature, it is relatively weak. In other words you change the temperature and you don't change the collision rate very much but you do change the probability of getting over the hump. So, this thing has a relatively weak temperature dependence.
If we put all of this together we have that the rate is equal to the fraction of successful collisions times the collision rate, which is p times f, which is the steric factor times this energetic factor times Z times the concentration of A times the concentration of B. Notice that we can lump p and f and Z into k. That is the rate constant, and A and B are just the concentrations of A and B. So, k equals this expression, the steric factor times the factor that depends on the probability of getting over the hump times the fudge factor for the collision rate, so we can say that k is equal to A, which is the p and the Z times the f, which is exponential .
What we are going to see in the next tutorial is the temperature dependence of k. So, k we've been saying is a constant, and it is a constant so long as temperature is not changing. But when the temperature changes, k changes; A and B don't change. The concentration of A and B don't change, but k is going to change. What we are going to see in the next tutorial is what impact that has on the rate of reactions.
Chemical Kinetics
Temperature and Rates
The Collsion Model Page [3 of 3]

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