# Rates of Chemical Reactions

Synopsis

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.

Review Question

1. What property would you choose to measure as a function of time to determine the time rate of loss of HCl when it is reacted with NaOH? Write the rate expressions for all four components.
2. Hydrogen peroxide decomposes to water and oxygen. Write the reaction and write the rate expressions for the three components so that they are equated to each other as we did above (eq. 1). What would you choose to measure in this reaction so that you could make a graph like the above for the decomposition of sucrose? Put your answer to this question, and how you would set up the experiment so that you could make the measurements, on the bulletin board of WebCT.
3. Use the graph for the decomposition of sucrose to estimate the instantaneous rate of decomposition of sucrose at 2 hours, 4 hours, and 8 hours. What can you deduce from these instantaneous rates?

Web Author: Dr. Leon L. Combs