lecture 25

# lecture 25 - Chemical kinetics We saw that the...

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Unformatted text preview: Chemical kinetics We saw that the equilibrium constant K of the reaction N2 + 3H2 = 2NH3 is large at room T and atmospheric pressure. Yet if you mix hydrogen and nitrogen under those conditions, nothing will happen. Thermodynamics tells us what the equilibrium is but nothing about how fast equilibrium is reached. Most interesting phenomena in chemistry and particularly in biochemistry are nonequilibrium processes. The speed at which chemicals react is studied by chemical kinetics. How to define the rate of a chemical reaction. We need a quantitative measure of how fast a reaction occurs. If I have some quantity x(t), the rate of its change is usually defined as v = dx/dt If, for instance, n(Ai) is the number of moles of chemical Ai then the rate of a reaction can be written as dn(Ai)/dt. However this way we would have 3 different definitions for the rate of the above reaction, dn(N2)/dt, dn(H2)/dt , and dn(NH3)/dt. Which one to choose? None. We have learned before that the progress of a reaction can be described in terms of a single variable, the extent of reaction ξ. We have dn(A1)/ν1 = dn(A2)/ν2 = … = dξ It is then natural to write, for the rate of a chemical reaction, R = dξ/dt However there is one more problem. Suppose I have 1 mole of nitrogen and 3 moles of hydrogen, and you have 100 moles of nitrogen and 300 moles of hydrogen. If you and I mix our reactants at the same T and P, it will take the same time for you and me to convert our ingredients into products. Yet our definition of the rate will tell us that your rate is 100 times greater than mine, which makes no sense. This is because the proposed rate definition is an extensive quantity. To fix this, we have to divide our rate by some other extensive quantity. For example, we could use mole fractions x(Ai) instead of n(Ai). A more common (and much better) approach is to use the molarities: [Ai] = n(Ai)/V where V is the total volume. The definition of the rate that we will use is therefore: R = V ­1dξ/dt = d[Ai]/(dt νi) Irreversible 1st order reactions Two types of reactions 1. A →B (example: isomerization, protein folding) 2. A →B+C (example: decomposition, CH3CH3→2CH3) are often described by the equation of the form d[A]/dt =  ­k[A] (1) Reactions that obey this differential equation are called first order reactions. Eq. 1 is called the first order rate equation. The quantity k is generally a function of P and T: k = k(P,T). It is called the rate constant. Note that reactions of the form 1 and 2 are not necessarily first order reactions (we’ll see why soon). But they can often be. Eq. 1 is very common in chemistry and physics. It describes a process, in which the rate, with which some quantity changes, is proportional to that quantity itself. Many other processes (e.g., population growth, light absorption etc.) are described by this type of equations. Physically, the rate constant k describes the probability, per unit time, for an individual molecule A to undergo the transition to B. Indeed, if we have NA molecules of A, then NA k dt molecules will undergo the transition to B. Therefore –dNA = NA k dt , which is equivalent to Eq. 1. The solution of Eq. 1 is [A](t) = [A](0) e ­kt Recall that we defined the rate of a reaction in terms of the extent of reaction ξ. We have d[B]/dt =  ­ d[A]/dt = dξ/V = dη where I introduced a new variable, η = ξ/V. Assuming that η(0) = 0, we find [A] = [A](0)  ­ η or η = [A](0) ­[A](t) = [A](0)(1 ­e ­kt). Using this equation, we finally find [B](t) = [B](0) + η = [B](0) + [A](0)(1 ­e ­kt). For the decomposition reaction (the second example), we also find: [C](t) = [C](0) + η = [C](0) + [A](0)(1 ­e ­kt). ...
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## This note was uploaded on 04/24/2011 for the course CH 52635 taught by Professor Makarov during the Spring '11 term at University of Texas.

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