In chemistry, kinetics is the study of how fast a reaction proceeds. In more proper terms, kinetics is the branch of chemistry dealing with rates of reactions and how they can be manipulated.
The Haber process, which we've discussed ad nauseum at this point, is an example of using kinetics for real-life purposes.
`N_(2(g)) + 3H_(2(g)) ↔ 2NH_(3(g)) + "heat"`
If we wanted to synthesize as much ammonia as possible, we could utilize Le Chatelier's principle; raise the temperature up to `400-450°C` and increase the pressure to approximately `200 "atm"` . While this in theory should drive the reaction far to the right, in practice the yield is found to be incredibly low. Why is that?
It turns out that while the reaction is thermodynamically favored, it is not kinetically favored. In other words, even though `DeltaG<0` for the process, the actual rate at which the reaction occurs is so slow that the reaction isn't noticeable.
The concept of thermodynamic stability vs. kinetic stability is one that comes up fairly often in chemistry. It turns out that only by adding an iron catalyst to the reaction chamber does the Haber process occur at a practical rate. By studying kinetics, we learn how we can affect the rate of reaction through altering various parameters such as catalysis, temperature, concentration, etc.
A rate is a concept seen very often in science. Rates are defined as "the change in something per unit time". An everyday example can be found in physics, where velocity (speed) is defined as the change in position per second , or `(Deltax)/(Deltas)` .
For chemical reactions, we define the rate of reaction as the "change in concentration per second," written as `(Delta[C])/(Deltat)` where `[C]` is the concentration of the species. The `Delta` , pronounced "Delta," represents the "change in" and is just a simply way of writing "Final - Initial." Thus, `Delta[C]` just represents the "Final concentration - Initial concentration."
The rate of reaction for a species represents how quickly the species is being consumed or formed. If the species is being consumed, the rate expression will be negative. Conversely if the species if being formed, the rate is positive.
To help illustrate this, consider the mock reaction `A + B ↔ 2C` . The rate expression for `A` would be written as:
`"rate of A" = -(Delta[A])/(Deltat)`
Where `Delta[A]` is the final concentration of `A` minus the initial concentration of `A` . Notice that the rate is negative. This is because we're assuming that the concentration of `A` is going to decrease in order to form products. In general, the rate expressions for reactants will be negative and the rate expression for products will be positive.
What if we wanted to figure out how quickly `C` was forming, but were only given the rate of `A` ? Let's say that the rate expression of `A` is `(-0.3M)/s` . What would the rate of `C` be?
According to the stoichiometry, for every `"mol of" A` that reacts, `2 "mols of" C` should be formed. The rate follows the same stoichiometric principles. Thus, we can express the rate of formation of `C` in terms of the rate of `A` :
`"Rate of" C= -2*("Rate of" A) = -2*((-0.3M)/s)=(0.6M)/s`
As mentioned before, the rate expression for the formation of `C` must be positive since the concentration is increasing over time. The negative is there to ensure that the rate expression of `C` ends up positive.
We can relate the rate expressions of all of the species by taking into account stoichiometry:
`"Rate of A" = "Rate of B" = -1/2*"Rate of C"`
`((-0.3M)/s)=((-0.3M)/s)=-1/2((0.6M)/s)`
From this, we can see that all the rates of the species in a reaction are related by stoichiometry.
For practice, here's a quick problem related to rates:
#1. For the reaction `A + 2B ↔ 1/2 C + D` , the rate of `C` is given as `(0.2M)/s` .
a) What is the rate expression of A?
b) What is the rate expression of B?
c) What is the rate expression of D?
We can find the rates just by using the stoichiometric relations between the species. We know that:
`"Rate A"=1/2*"Rate B"=2*"Rate C"="Rate D"`
Rearranging these, we can get that the `"Rate A"=-2*"Rate C"` , or that `"Rate A" = -2*"Rate C"`. This means that `"Rate A"= -2*((0.2M)/s)=(-0.4M)/s`
We can find the rates just by using the stoichiometric relations between the species. We know that:
By rearranging the expressions for `A` , `B` , and `D` , we can solve for the rate expressions of each.
Answer: a) `(-0.4M)/s` b) `(-0.8M)/s` c) `(0.4M)/s`
One last thing to note is that the rate of a reaction varies over the course of the reaction. As the reaction goes on, the rate of the reaction can change drastically. A typical graph of reaction rate vs. concentration looks like this:
What the graph is showing is that the reaction rate at low concentrations is low, but as the concentrations increase, the rate grows rapidly. What we're measuring in rate expressions is usually called the instantaneous rate because it's the rate at a certain instant. For example, a reaction may start off with a rate of `(3M)/s` and over time slow down to `(0.3M)/s` . When we write rate expressions, we usually are describing the rate only at a specific instant.
1. Kinetics is the study of rates of reaction and their manipulation.
2. The reaction rate of a species is the change in concentration per second and is calculated through `(Delta[C])/(Deltat)` .
3. The rate expression for reactants is negative because the concentration of reactants decreases as the reaction proceeds. The rate expression for products is positive because the concentration of products increases as the reaction proceeds.
4. The rates of the different species in a reaction are related through their stoichiometric coefficients.
5. The rate of a reaction can vary with the extent of the reaction. Rate expressions tend to express instantaneous rates, or rates at a particular instant.
#1. Thermodynamics vs. Kinetics of Diamond/Graphite
The thermodynamically stable form of carbon is graphite, which is the main ingredient in pencil lead. Given enough time, all diamond will convert to graphite.
The reason that we don't observe this is that the reaction is kinetically limited. In other words, the conversion is so slow that it would take millenia to even notice a slight change. We can be sure from calculations that the conversion is happening, just at a negligible rate. With this knowledge, we know that diamonds actually are not forever.
By the way, we can speed up the kinetics of the conversion by increasing the temperature of the reaction. If we were to leave a diamond sitting in a room, it may take billions of years before it converts to graphite. If we were to leave the same diamond in a room at a very high temperature, the rate would be significantly lower - perhaps even noticeable.
#2. Calculus
If you've taken calculus, the concept of an instantaneous rate may sound familiar to you. After all, an instantaneous rate is just a derivative! Since not everyone has taken calculus at this level of chemistry yet, the calculations are simplified such that we can understand the concepts without diving too much into the math. The cool thing about kinetics is that nearly every expression can be derived through simple calculus, since kinetics deals almost entirely with instantaneous rates.