Hello, in this video we're going to start talking about chemical reactions. In this particular first video of this module we're going to specifically talk about what a reaction is, reaction rates, and the reaction rate constant. So what is a chemical reaction? Well, it's a collisional process in which the atomic composition of atoms and molecules change and here is an example of such a reaction. CH3 is called the methyl radical, hydrogen atoms called the hydrogen radical. Both of these are so-called radical species and we'll get into that in a bit and M could be any other molecule. So in this particular example, if the reaction goes from the left to the right, it means that the methyl radical and hydrogen collide, they form methane. But it just turns out that in this kind of reaction if there was no way to absorb some of the extra exothermic energy that that reaction involves then they just immediately fall apart so that M could be any other molecule that just absorbs some of that energy. And so the products would be methane CH4 and the unchanged third body or the reaction could go in the other direction. You could have methane and it could be hit by some other molecule and it could knock a hydrogen off. In any event, the result of the reaction is there's a shift in the distribution of the atoms, but the atoms are conserved. So and this is reflected in the coefficients in the equation. This is this equation has 1s in front of each of the chemical symbols, but clearly if you start out with one carbon on the left side, you have to end up with one carbon on the right side. And that's reflected in the little table that lists the carbon, hydrogen, and M, whatever M may be, balance. And so the table lists the atom and it lists the number in the reactants and the number in the products and they have to be the same. There's 1 carbon, 4 hydrogens and 1 M, whatever M may be, and so they do balance. If you count up on the left side the hydrogen, there's 3 in the CH3 and then 1 that's free so that's 4. And on the right hand side there's 4 in the methane molecule. Now it's important to recognize that one sees two types of chemical reactions written. The first is what's called an elementary reaction. An elementary reaction is one that actually occurs in a single step. So the example here is O atom colliding with hydrogen molecule and knocking one of the hydrogens off of the H2 and oxygen attaching in its place, so you'll form + H. Global reactions are reactions we often write. In undergraduate thermo, if you've got to combustion, you will written an equation similar to the one on the bottom of the slide. That's CH4 + 2O2 goes to CO2 + 2H2O. That's the global overall reaction of the oxidation of methane with oxygen. And again, if we count there's 1 carbon on each side, there's 4 hydrogens on each side and there's 4 oxygen atoms on each side. Here are some additional examples of elementary reactions. The first is a unimolecular decomposition of acetylene. And that's where acetylene falls apart into CH2 + C. In a more formal way of writing that reaction there'd be an M on each side because of course acetylene isn't going to fall apart all by itself. It's going to get whacked by some other molecule and that will cause a carbon to detach. The next reaction is called a bimolecular reaction because there's two reactants involved. In this example there's an O atom and H2 and this is essentially this is the same reaction I showed on the previous slide where O and H2 collide and one of the Hs is traded out for an O. And then the third example is so called trimolecular reaction where you have three reactants that come together, CH + CO + M produces HCCO + M. So there's unimolecular reactions, bimolecular reactions, and trimolecular reactions. You might notice that in the trimolecular reaction the reaction that goes from right to left, M colliding with HCCO, that is a unimolecular reaction. And that is often the case that the two different directions, one direction of a unimolecular reaction is unimolecular, the other direction would be trimolecular. And so those are the typical kinds of reactions that you see. Now those are reactions, what about how fast reactions occur? How do we express that? Well suppose we have aA +bB goes to cC + dD. They have some coefficients in front of them that reflects their composition and make sure that the number of atoms on the left equals the number of atoms of the on the right of each type. Those lower case letters are called stoichiometric coefficients. And it turns out that the overall rate of reaction which is a concentration per unit time can be written in the following fashion. Clearly if we write the overall rate of reaction as the rate of going from the left to the right, then A is decreased, B is decreased, C is increased, D is increased. So we have R = -1 over a d[A]/dt or -1 over B, d[B]/dT or plus 1 over c d[C]/ dT or 1 over d d[D]/dt. Just note that the notation for concentration is the molecular symbol in square brackets. And that's amount of material per unit volume and it could be number of molecules per unit volume or moles of molecules per unit volume, but it always on a number or molar basis. How about how fast the reaction occurs? Well, this is an expression that the slide I just showed us gives an expression for the rate reaction but it doesn't say much about how it actually goes. The reaction rate can be shown to usually depend on the concentration of the reactants. Generally the reaction rate is written as lowercase k which is called the reaction rate constant times the concentration of A to some m power plus B to some n power. And if it's an elementary reaction, that m and n are the stoichiometric coefficients of A and B. And this is called and this produces what's called a rate equation or rate expression. And you can write it symbolically as the equation below. Again k is the reaction rate constant. So here's an example. Here's an elementary reaction, one that I showed before, O + H2 goes to + H. There will be a reaction rate constant for each direction and I've labeled them above and below the arrows here as kf forward and kr for reverse. Sometimes you'll see if you have a number of reactions, say the first reaction might be k1 for forward and k-1 for back. It's just a different notation. So then the rate expression for say the destruction of O atom as a result of these reactions d[O]/dt is going to be equal to minus k forward times the concentration of O times the concentration of H2 plus k reverse times the concentration of Times the concentration of hydrogen. Now often time especially in early days, less so nowadays, where people didn't understand very much about the details of the chemistry that took place in these kinds of combustion reactions, they would write the global equation, global reaction. So this is propane burned with oxygen. So we have propane + 5O2 produces 3CO2 + 4H2O. And then they would experimentally study how fast this reaction occurred and they would come up with some kind of rate expression for it. And this is an example so that the rate of destruction of propane is equal to minus k times the concentration of propane to the 0.1 times the concentration of O2 to the 1.63. So what about the reaction rate constant? The reaction rate is determined by the rate at which reactants collide times the probability that a reaction will occur. And experiments show that many rate constants are of the form shown where k is equal to some constant a times the temperature to a power n times e to the minus an energy over RT, the energy is called the activation energy, R is the gas constant. T the temperature, A is the pre exponential or frequency factor and often the value n is something other than than zero. So why does this make sense? Well, the activation energy is the energy required for the reaction to occur, and we'll explore this in more detail in a later video. But this little diagram shows that if you have reactants that are of a certain energy and you want to produce products you may have to provide an amount of energy shown by this curve, which I've labeled the activation energy for the reaction to occur. In other words, you have a molecule, it's stuck together with inter-atomic forces, you've got to overcome that force in order to pull the molecule apart and rearrange it with other atoms. Note that if the activation energy is zero then that exponential term goes to zero and the rate is just some number and what that number is is the collision frequency basically. Because it if the activation energy is zero pretty much any collision can cause a reaction. In the world of chemical reaction rates the way people study this is that they calculate the energy of a particular molecule. One I've labeled A here, and then they've calculated how much energy would be required in order for it to turn into a different molecule B in this example. And then they produce a diagram like this which is called a potential energy surface or potential energy diagram. And so in this particular example of A going to B, the activation energy is the difference in energy of the A molecule and the energy of the highest energy configuration that the molecule goes through in converting to the B molecule. That's the activation energy. Now there is a simplification in terms of calculating reaction rate constants that comes about because of detailed balance. We talked about detailed balance early earlier when we talk about chemical equilibrium and the chemical equilibrium constant. It does turn out that if local thermodynamic equilibrium applies, then detailed balance applies regardless of whether there's chemical equilibrium. And what that means is that the forward reaction rate constant and the reverse reaction rate constants of an elementary reaction are related by a simple function of temperature. And it turns out that that really makes things a lot easier if you have a particular reaction and it's easier to study in one direction than the other you study it in that direction and then you use detailed balance to get the reverse rate. And also in computer codes, virtually all the computer codes that are out there, you only have to provide the rate constant information for one direction, and then they use detailed balanced to get the other direction. So that's it for this video. Thanks for listening and have a great day.
