Reading Notes for Chapter 12


These are Dr. Bodwin's reading notes for Chapter 12 of "Chemistry 2e" from OpenStax. I am using a local .pdf copy that was downloaded in May 2020.

Chapter Summary:

Kinetics is the study of rates and mechanisms. Rates are how fast a reaction happens, mechanisms are how a reaction happens.

Start with Theory:

Different books and sources have different approaches when it comes to presenting theory vs application. I lean toward a "theory first" approach, especially when looking at kinetics, because starting with "why" can often give context to a bunch of the "what" topics. If we want to study kinetics, the first question that we really have to ask is, "Why do chemical reactions occur?"

Collision Theory (Section 12.5):

The name kind of gives it away, but chemical reactions occur because collisions occur. For the generic reaction:
A  +  B   -->   C
It is not possible to form C if A does not interact with B, and we call that interaction a collision. To make this easier to visualize, let's start with a gas-phase reaction where there is just one A particle and one B particle held inside of a container. A and B will bounce around the container (look back at the Gas chapter to review some of this info) until they hit one another. Does that mean that C will form? Maybe. There are a couple specific condition we have to kepe in mind:
  1. Collisions must occur
  2. The collisions must be sufficiently energetic to allow reaction
  3. The colliding particles must be oriented in such a manner that the desired reaction can occur
Keeping those points in mind will help us understand a LOT of kinetics! Collision Theory (and kinetics) is all about probability. Let's take a closer look at each point:
1. Collisions must occur
This is the basic part. A and B have to interact. How can we affect how often they interact? Or stated differently, how do we increase the probability of a collision occuring?
2. Collisions must be energetic
Just because 2 people happen to bump shoulders in a crowd doesn't mean they will react to one another. Similarly, A & B have to collide with sufficient energy to (momentarily) mash their electron clouds togetherto allow an electron rearrangement to occur. {This "electron rearrangement" is a chemical reaction!} Again, this is a probability step... there are a LOT of collision, but only a certain percentage of them are sufficiently energetic to cause reaction. If we increase the temperature, the reactant particles will move faster, and the faster they move, the more energetic their collisions will be. Similarly, if we increase the number of A & B particles, there is a higher probability that a collision will be sufficiently energetic to react.
3. Collisions must be oriented
Have you ever tried to connect a trailer to a vehicle? There's only one way to orient the trailer and the vehicle that can lead to a successful coupling. Pulling your truck up to the side of the boat just doesn't work. Similarly with chemical reactions, the colliding particles have to be oriented in such a way that reaction is possible. If a sodium atom is reacting with a chlorine atom, there's probably not much of an orientation effect because both are (mostly) spherically symmetric, but most reactions have a strongly preferred orientation. Again, it's a probability thing... if the "front" of A has to collide with the "side" of B, then there are a bunch of collisions that will not be productive. Increase the number of collisions, increase the number of properly oriented collisions.

For the sake of argument, let' say that A & B collide 10% of the time. Of those collisions, let's say that 30% are sufficiently energetic to cause reaction. That's (0.1*0.3)=0.03=3% of the time that collisions occur and are sufficiently energetic. Now let's further say that 40% of the collisions are correctly oriented to cause reaction. That's (0.1*0.3*0.4)=0.012=1.2% of the time that collisions occur and are sufficiently energetic and oriented for reaction to occur.

Reaction Rates:

What is a "rate"? The most general description is that a rate is a change in some measurable property over a change in time. There are a bunch of "measurable properties" that we could measure, but for chemical kinetics we usually measure the change in concentration of reactants and products.
One of the biggest benefits of a balanced chemical equation is that gives us a relationship between reactants and products. If it takes 2.83minutes to react 1 mole of A, then it also takes 2.83minutes to react 1 mole of B, and 2.83minutes to form 1 mole of C! This gives us a HUGE advantage because it is often difficut to measure the concentration of a chemical substance during a reaction, but as long as we can observe and measure any one reactant or product, we can know the rate of consumption or formation of all the reactants and products.

Average vs Instantaneous Rates:

This may sound a little like calculus, but don't worry, it's not! {Well, it is, but don't let that get you all twisted up in knots...}
An "average rate" is the rate over a "long" period of time. If you change the period of time, the rate is different. In some cases, average rates work great, but they all have the challenge that changing the time period changes the rate.
An "instantaneous rate" is the rate at a single moment in time. For the calculus folks, it's the tangent line to the concentration curve... also known as the derivative. But you don't really have to know derivatives to understand instantaneoud rates. Instantaneous rates also change at every moment in time, but they give a nice snapshot of what is happening as the reaction occurs.
SIDE NOTE: There's a magic negative sign that appears and disappears in reaction rates. Why is that? Is it truly magic? Nope. By its nature, a "rate" of a chemical reaction is always thought of a positive. Or, perhaps more specifically, a chemical reaction rate is a magnitude of change over time, not a direction of change over time. When we look at a "delta function", the formal definition of that is "final condition minus initial condition". For a reactant, the final concentration is smaller than the initial condition, so the "final minus initial" is negative. But rates can't be negative, so we add a negative sign. If we're looking at a product, the final concentration is larger than the initial concentration, so "final minus initial" is positive, so we don't need the negative sign.

Rate Laws:

Look at Figure 12.5 in your textbook. This is a ncie example of a "concentration vs. time" graph for a chemical reaction. At any point on those curves, we can determine an instantaneous rate. That's a lot of rates. But there is one unique point (or rate) on those curves... every point in those curves has another point to the left of it and the right of it except... the initial point. As long as we know where to start, we can calculate the curvature of the concentration vs. time graph, but that initial point is crucial.
To start our discussion of rate laws, let's go to an even simpler reaction:
D  -->  E
That's it. One reactant forming one product. It doesn't get much simpler. If I have a single D particle in a bottle, it will bounce around until it has the right collision with the wall of the container for a reaction to occur. The rate of this reaction is directly related to the size of the container; or another way to say that is it's directly proportional to the concentration of D.
Raterxn ∝ [D]i  
Proportionalities are nice in concept, but they're not so useful in math... we can change that to an equality with a proportionality constant, let's call it "k"
Rateinitial = k[D]initial  
That's a rate law expression. A rate law expression describes the initial rate of a reaction in terms of its reactants raised to a power that is determined by the collisions that occur in the reaction. For any reaction, we can write a rate law expression if we know the reactants involved, although to start with there will be a LOT of unknown variables. For our favorite test reaction, A + B --> C, the rate law expression is:
Rateinitial = k[A]ix[B]iy
For our purposes in this class, "x" and "y" will only have the values of 0, 1, or 2, and these values must be experimentally determined. Let me repeat that: MUST BE EXPERIMENTALLY DETERMINED. These exponents are called orders of the reaction, and indicate the number of each particle that is involved in the collision that determines the rate of the reaction.
Hold on! What?!?!
OK, let's go back to collisions for a moment and talk about probability again. If a particle has to collide with a wall, that seems like it might not be too hard, but what if A has to collide with B? That seems like it would have a smaller probability than if A just had to collide with a wall. And don't forget, the collision has to occur, AND it has to be energetic, AND it has to be oriented. What it we propose that three particles have to collide to make a reaction occur? That seems less likely. And f those 3 particles have to collide, AND the collision has to be energetic, AND the collision has to be oriented, then it seems VERY unlikely that it will occur... the probability is likely so low that we can say it "never" happens. SO the orders of the reaction tell us how many of each particle are involved in the collision that determines the rate of the reaction.

Reaction Mechanisms:

What if we have a reaction such as:
2 F + 3 G + 2 H ---> products
{Because rate law expressions only deal with reactants, it's not really that important to include specific products here.}
From our collision discussion, we know that these particles can't all react by a single collision... that would require SEVEN particles to collide, AND be energetic, AND be properly oriented... that's not going to happen. So there must be a series of collisions involving fewer particles that add up to the overall reaction. In fact, that is the definition of a reaction mechanism... A reaction mechanism is a series of elementary reactions (unimolecular and/or bimolecular collisional steps) that:
  1. When added together yield the overall chemical reaction
  2. Is consistent with the observed rate law expression for the reaction
So for the above reaction, the rate law expression is:
Rateinitial = k[F]ix[G]iy[H]iz
The values of x, y, and z must be determined experimentally. For every reaction, there is a rate limiting step or a rate determining step that ultimately defines the rate law expression. I'll use both terms when I'm talking about this, but I will use "RDS" as shorthand when I'm identifying a Rate Determining Step. Think of the RDS like a construction zone on a highway... Traffic might be moving at 60mph before the construction zone and 70mph after the construction zone, but the total time of your trip is going to be determined by the construction zone where traffic is moving at 5mph. Or if you start a cooking-making business and your oven can only hold 1 pan of cookies at a time... you might be able to mix up the dough pretty quickly, and package the cookies quickly, but the baking and cooling step will slow down your overall process - it's the RDS. That's why the order of a reaction can be zero with respect to some reactants... if those reactants are not part of the RDS, they may not have any impact on the rate!

Determining Rate Laws:

The easiest way to experimentally determine the orders in a rate law is by the method of multiple trials under different concentration conditions. Process takes practice, so make sure you take advantage of any opportunities. In your textbook, Example 12.5 walks through a relatively simply example. A couple notes about solving these problems:
Don't take shortcuts until you're confident in the "long way" to do the problem. After you set up a few dozen of these problems, you'll start to get comfortable enough to estimate the orders, afterall, they are limited to only 0, 1, or 2. Qualitatively, if you see that the rate triples when the concentration of A triples (and no other concentrations or conditions change), then you know that the reaction must be 1st order with respect to A. But don't try to use the shortcut without setting up a bunch of these problems mathematically first.
NOTE: There's nothing magical about the number 2. Many textbooks will systematically change concentrations by multiplying or dividing by 2. They do this because they are lazy and it's easy. The exact same rules and process apply for factors of 3 or 4 or 1.25 or 3.374.

Integrated Rate Laws (IRLs):

Your brain should be tingling here... yout textbook shows a chemist doing a bunch of math to a perfectly lovely expression... why? Why do chemists do "extra" math, especially extra calulus math? Because they're trying to force something to be a line because lines are easy to understand.
"Regular" rate law expressions are packed full of information, but one thing they are not good at is predicting concentrations as time passes because there is no time component in the rate law expression. {Yes, time is part of the rate, but that's difficult to use in a regular rate law expression...} By doing a little calculus, we can get an explicit time factor in the equation. That's what an integrated rate law expression is good for.
You need to know the order of the reaction with respect to the the reactant of interest so you know which integrated rate law expression to use.
Using IRLs, you can also determine the orders with respect to a given reactant. Check out Example 12.7 for a good example.

Recognizing Different Problem Types:

This chapter has a lot of different problem types that look just similar enough that it can be hard to know what type of problem you're doing. Here are some things to look at...
These are just a couple things to look for. the best way to recognize these is to practice.

Activation Energy:

Activation energy is the hill that we must get over when going from reactants to products. It determines the rate of the reaction. If there's a big hill, the reaction is slow; a small hill and the reaction is fast. Figure 12.14 in your textbook shows this hill as part of a reaction coordinate diagram.
Arrhenius Equation - The "short" form of the Arrhenius equation, as shown on page 686 of your textbook, is a lovely little equation, but it is minimally useful in that form. It's much more useful in its linear (p688 of your textbook) or comparative form.

Catalysts:

Catalysts increase reaction rates but are not consumed by the reaction. They do this by changing the mechanism in a such a way that the activation energy is lower.
Homogeneous catalysts are in the same phase as the reaction. They tend to work well because they can mix very effectively with the reactants. Big disadvantage - they can be hard to remove from the reaction mixture.
Heterogeneous catalysts are a different phase or are immobilized on a different phase. Steps must be taken to help them mix effectively with the reactants, but they are (relaively) easy to remove when the reaction is done.
In biological systems, enzymes are catalysts.




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