Lecture Notes
These notes should act as supplements to the lecture material presented during weekly meetings. Great for catching up on make up work or reviewing previous material.
See attached! -Your ChemClub Officers
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Here's the powerpoint from our meeting yesterday. Problem set will be posted soon - let us know if you have any questions!
Powerpoint for your reference!
Notes on Steady State Approximation from today. There's even a biology question related to enzymatic rate at the end for you biology fanatics! :D Practice problems with solutions will be uploaded soon under the resources tab. Let us know if you have any questions!
In preparation for this Thursday's lecture on Advanced Kinetics, please take a look at this worksheet and think about/complete the attached problems.
Today's Presentation: https://docs.google.com/presentation/d/1YdHsgWy2_o6OWkUJ0xeakbN1P6cOS0E2lWtE_UjbxaU/edit?usp=sharing
Kinetics Worksheet is found under the Resources tab. Let us know if you have any questions about anything! Inorganic Chemistry
Concepts
Equilibrium, as defined by the Webster Dictionary, is "a state in which opposing forces or actions are balanced so that one is not stronger or greater than the other." This same definition applies to chemical equilibrium systems. For any chemical reaction, reactants react to form products. However, those same products can also react to recreate the reactants. Both of these reactions - the original forward reaction and reverse reaction - have some amount of "chemical force of favorability," meaning that due to the nature of the bonds between the molecular species, the formations of either the products or the reactants both have some sort of drive to try to achieve the state of lowest potential energy, also known as balance or equilibrium. Chemical equilibrium is also called a dynamic equilibrium. This means that after the state of lowest potential energy, the molecules don't just stop reacting. The forward and the reverse reactions are just occurring at equal kinetic rates such that there is no net change in the concentration of any of the molecular species. aA + bB ⇌ cC + dD where A, B, C, and D are the molecular species and where a, b, c, and d are the respective coefficients. This notation actually represents two different reactions occurring at once:
Combustion reactions are very common. The combustion of propane, a hydrocarbon, is a common reaction, as propane is common fuel used for BBQs. The reaction can be represented as an equilibrium system: C3H8 + 5O2 ⇌ 3CO2 + 4H2O This means that the combustion of propane (C3H8) does occur, but theoretically, the reverse reaction, where carbon dioxide and water vapor react to form propane and oxygen gas, does occur, too. However, this reverse reaction occurs to such a small, infinitesimal extent that it has pretty much no impact on the concentrations of species, and the reaction occurs in the forward direction basically to completion. That is why the reaction is most commonly (and should be) represented as C3H8 + 5O2 → 3CO2 + 4H2O. However, even though the reaction occurs to completion (meaning all of the reactants react completely following stoichiometric laws), this can still be argued to be an equilibrium system. This combustion reaction demonstrates a few very important point in chemistry:
For the reaction aA + bB ⇌ cC + dD, the Law of Mass Action is the Keq mathematical expression shown above. Essentially, its a ratio between the product of concentrations of the products raised to their respective coefficients and the the product of concentrations of the reactants raised to their respective coefficients. The concentrations of reactants and products that you plug into the Keq Law of Mass Action expression are the concentrations at the equilibrium position. The law of mass action gives chemists a lot of information about equilibrium systems. For example, if the calculated Keq expression gives a number greater than 1, then the forward reaction to produce the products C and D are chemically favored. If the calculated Keq expression gives a number less than 1, then the reverse reaction to produce the reactants A and B are chemically favored. What determines chemical favorability? The answer literally lies within the bonds of the molecular species. Each bond between two atoms has a characteristic average amount of potential energy. The equilibrium state occurs when the bonds of the reactants and the bonds of the products have the same amount of potential energy stored. In this sense, a reaction is chemically favorable if it is conducive towards reaching that state of equal potential energy. A common misconception is that equilibrium always occurs when the number of products equals the number of reactants. Nothing could be further from the truth. Equilibrium is a measure of potential energy state, meaning that at equilibrium, potential energy is equal. The products and reactants will almost always have differing concentrations to achieve this state of total minimization of potential energy within the chemical system. Le Chatelier's Principle is very important when it comes to equilibrium. Its states that whenever one applies stress to an equilibrium system, the system will move in the direction to relieve the stress. This means that if you add some additional molecular species, the reaction will either move in the forward or reverse direction by either consuming or producing products to reestablish the same ratio of reactants and products. In essence, the Keq value always remains the same no matter what, except for temperature changes. For example, let's say I have a machine that can turn pens into pencils and vice versa. In my school supplies case, I am very picky and like to always have a constant ratio of 2 pencils per every 3 pens in my case. Currently, I have 10 pencils and 15 pens. Now, one day, my parents give me a birthday present of 10 more pencils. Now I have 20 pencils and 15 pens, but this upsets me because the ratio is now imbalanced. Because I have received an influx of pencils, the additional number of pencils places stress on my case/system, which can be relieved by consuming some pencils and producing pens. In this case, if I use my machine to convert 6 pencils into 6 pens, I will now have 14 pencils and 21 pens, thereby reestablishing my desired ratio and making me happy again! Le Chatelier's Principle is all about preserving a constant ratio between species. The amounts of products and reactants are always subject to change in a volatile environment, but what's important is preserving the ratio, or Keq value, of an equilibrium system. That's all of the conceptual background behind equilibrium and Le Chatelier's Principle. Remember, all reactions are systems of dynamic equilibrium that strive to preserve balance through a constant ratio of products and reactants and a drive to find the point of lowest potential energy.
More information about the math behind all of this can be found in this week's handout or at this link: Equilibrium Calculations. Kinetics is the study of rate and how fast a reaction proceeds to either completion or its specific equilibrium state. In other words, kinetics measures the speed of a reaction. The speed of a reaction is affected by 5 things: the concentration of reactants, the temperature at which the reaction takes place, the phase/surface area of the reactants, the presence of appropriate catalysts, and the solvent of aqueous reactions. As concentration increases, reaction rate increases. There are more reactants in the chemical system, so there is a higher likelihood, or probability, that the reactant species will collide in the just the right way to create the reaction. Think about it - where is it more likely that two random people are going to accidentally bump into each other: in a room of ten people or in a room of ten thousand people? As temperature increases, reaction rate increases. Higher temperature means a higher average velocity of all the chemical species, so there is a higher likelihood that the reactant species will collide with enough activation energy to proceed forward with the reaction. If I tap someone lightly on the shoulder, nothing really happens. However, if I punch someone as hard as I can, I'm certainly going to create some sort of reaction! This is because I put more energy into "getting their attention." (Please don't try this at home.) As the surface area of solid reactants increases, reaction rate increases. Increasing surface area exposes more molecules that are able to be reacted. Which is easier/faster - dissolving a block of sugar or the fine granules of sugar? Also, generally speaking, gases react the fastest while solids react the slowest. This is because gaseous molecules move around quickly and collide frequently. Contrast this to solids - they can't react if they aren't in contact, right? This is related to temperature and kinetic energy - the more kinetic energy a reactant phase has, the faster the reaction. The presence of an appropriate catalyst increased reaction rate. Look up the definition of a catalyst if this is still unclear. Remember that chemical catalysts work by providing an alternate pathway for a mechanism with lower activation energy than the original pathway. It does NOT "lower the activation energy of the reaction" - that's impossible! Finally, solvent properties affect the rate of aqueous reactions. This is not studied in depth in either Honors Chemistry or AP Chemistry, but it can still be helpful to know. Some solvents interact favorably with reactants or reaction intermediates, speeding up a reaction more so than other solvents. This is in part due to intermolecular forces and interactions (covered in future lectures - basically how species interact). Another important concept to cover - rate mechanisms. Let's consider the combustion propane, a common fuel source for outdoor barbecues. The reaction looks like C3H8 + 5O2 --> 3CO2 + 4H2O (Propane and oxygen gas react to form carbon dioxide and water). Let's think about this on the molecular level. Does one molecule of propane and five molecules of oxygen gas somehow all collide at once and instantaneously forms carbon dioxide and water? Of course not! The odds of that happening would be astronomically low, and we would never be able to eat our fourth of July hot dogs ever again! Rather, the combustion occurs via a rate mechanism - a series of small elementary steps that occur one after the other to ultimately lead to the overall reaction. The combustion of propane, like many reactions, has a very complicated mechanism, something we won't get into too much detail here. The most important thing to note conceptually is that elementary steps rarely ever involve more than three species colliding at once (and even three is rare, too). Mechanisms almost always include intermediates as well - chemical species that are produced from one elementary step but consumed in another, such that the net production of the species from the overall reaction is zero. If you are in AP Chemistry, please refer to Pt. 2 of the Kinetics Notes as well. Now that we understand the concepts behind kinetics, let's take a look at the math and related equations. A rate law is a mathematical equation that relates the rate at which a reaction takes place, usually written in the form of change of product concentration over a given time period, with the concentrations of reactants at a given point in time. These rate laws give the instantaneous rate at which product concentration is changing at a specific point in time. A differential rate law looks like Rate = k[A][B][C]... for some constant k and reactants A, B, and C. k changes with temperature. [A], [B], and [C] can be raised to any power (usually integer powers - fractional powers are very rare) and are called the order of the rate law with respect to the reactant. Order must be experimentally determined - they are NOT the coefficients of the balanced equation! An integrated rate law results when you integrate the differential rate law. There are three types of tested integrated rate laws: zeroth order, first order, and second order. See the figure above for the integrated rate laws and their corresponding differential rate laws. It is important to note that integrated rate laws only exist for single-species reactions; for this reason, differential rate laws are much more common.
To determine the rate law from experimental reactions, see: http://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/DifferentialRateLaws.html. |
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