The concept of "rate" is not a new one to most people. We talk about the rate at which we type and this rate is usually expressed as the number of words per minute. We talk about the rate of motion of our car, meaning the velocity of our car, which is expressed in miles per hour. These rates are determined by measuring the change in something that we can measure divided by the change in time during which the measured change occurred. We use the symbol ) to mean change as we have done previously. So the velocity of a car can be written as )d/)t where d is distance and t is time. We can apply this method to a chemical reaction, but we have to find something to measure that is changing. For the reaction
aA + bB --> cC +dD
we might could measure the rate of disappearance of A , the rate of disappearance of B, the rate of appearance of C, or the rate of appearance of D. So what property of A, B, C, or D do we choose to measure? Usually we would choose whichever property was the easiest to measure accurately. Whatever property we measure, we are measuring the concentration of the species, [A], as a function of time. We can equate the rates by dividing each rate by the stoichiometric coefficient:
rate = r = -1/a([A]/t) = -1/b([B]/t) = 1/c[C]/t) = 1/d([D]/t) ........eq.(1)
Now the rate of loss of A is equal to the time rate of loss of B, and they are both equal to the time rate of formation of C which is equal to the time rate of formation of D. This measurement of the time change in concentration of one reaction component will give us an average rate of the time interval. We can plot our measured value of the concentration of one component vs. time and for a component that is being consumed, we would have something like the following (this graph is for the decomposition of sucrose):
If we want to determine the instantaneous rate at a particular time, we would find that time on the x-axis, draw an intercept up to the curve, and then determine the slope of the curve y/x at that point.
Web Author: Dr. Leon L. Combs
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