On the opening day of your business, you give your workers a brief pep talk and then go up to your office and put your feet up on the desk. At the end of the day, you go down to the factory floor and discover that only 6 dolls have been made.
The next morning, you give your workers a stern talking to and then retire to your office and put your feet up on the desk, sure that things will go better today. However, at the end of the day, you discover that only 6 more dolls have been produced.
Pondering the failure of your pep talks to make your workers productive, you decide to sneak down to the factory floor and watch the process.
What you see is this:
- Doll torsos are moving into the main room on a conveyor belt.
- A woman standing beside the belt sticks two legs onto the torso.
- Next to her, is a man sticking arms onto the torso.
- Just down the belt is a college student sticking on a head,
- and at the end of the line is…
- an old man…
- dipping his paint brush into the paint…
- and carefully…
- very carefully...
- painting…
- each…
- separate…
- feature…
- of the face.
Of course not.
You can probably imagine that at this point, after three days of work, there is a pile of finished, but unpainted dolls piled up at the painter’s feet. The issue is not the production of the dolls (arm, leg and head sticking), but the painting of the faces. The only way to speed up the process is to speed up that step.
What you need to do, of course, is to hire more face painters.
Arm stickers, leg stickers and head stickers have no effect on the rate at all.
Only the face painter affects the rate, because he is SOOOOO much slower than any of the other steps. In fact, those steps could get faster (or even slower) and there would be no change in the rate of doll production.
We could write out a “formula” for the process of doll making, which would look like this:
However, it would be more helpful to look at the steps that occur:
The overall process (similar to a chemical reaction) takes place through a series of steps (together called a mechanism) and only by changing the rate of the slowest step (called the rate-determining-step) can we change the overall rate.
There are two ways that this process can be sped up. By changing the concentration (this has to do with order) and by changing the mechanism (this has to do with catalysts)
Understanding Order - the analogy continues...
Since the last step of the process is clearly the slowest, then anything that can be done to make that step faster will increase the overall rate. For instance if we doubled the number of workers painting faces we could double the rate of doll production, even if both painters were still slow and meticulous.
So, how does this explain 0th order? How can the concentration of a reactant have NO impact on the rate of the reaction? the answer is rather simple - only those things that are in the slow step can influence the overall rate of the reaction. Hiring more "arm-stickers" will have no effect on the rate of doll production. In the same way, the concentration of anything that does not appear in the slow step will not affect the rate of the reaction, and will therefore be zeroth order.
Understanding "get-involved" catalysts - The analogy continues...
It might be possible to speed up the process by changing it. Perhaps you could find a face stamp, with which a worker could quickly stamp the face onto the doll. In this way the process would be the same (torso + legs + arms + head + paint) but the slow step would be much faster, and thus the whole process would be faster. In this analogy, the face “stamp” would be a catalyst – providing a faster way for the slow step to occur.
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