respectively, where k1 and k2 are the rate constants for forward reaction and & and k_2 are those for backward reactions; a,b, and p are the molar concentrations of chemical species A, B, and P, respectively. Most chemical reactions are reversible, to a certain extent. It is customary to write a chemical reaction left to right with the forward reaction rate constants <k1 and k2) larger than those of backward reactions (k _ x and k _ 2). In measuring the initial rate of reaction (dp /dt)initiah that is, in the early stage of a reaction, because product concentration p is rather small, equations 1 and 2 are reduced to equations 3 and 4:

initial kxa k9ab

will change during a given period of observation. Or more simply, not one changing atom knows whether any one of the other unstable atoms in the sample population has decayed or not. The following example will illustrate how this condition leads to exponential decay. Consider a classroom containing 100 students; each one of them tosses a coin once a minute. Suppose that anyone who obtains a head is asked to leave the room. After the first toss, there will be approximately 50 people leaving; after two tosses, about 25 people leaving; and the number of people remaining in the room will decrease exponentially with time. Mathematically, the number of people, N, in the room, varies with time, according to the following equation (the negative sign recognizes the number is decreasing):

Separating the variables and integrating:


CN dN ft , , , 1T , , - -TTT = kdt; In N0 = kt + In N (7) JN0 N Jo

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