Speed of Reaction Concept Confusion

name         Justin
status       educator
grade        9-12
location     IL


Question -   I have been reviewing answers from open-ended
laboratory reports I assigned my students this past year.  I think
I may have confused them on the speed of a reaction versus the time
to the endpoint of reactants.  At this point, I need help
articulating what these concepts are.

I assign an experiment involving a pellet of baking soda and
powdered baking soda with vinegar.  The masses of baking soda are
the same, but I am trying to get across the idea that the one with
the greater surface area will react faster than the pellet (this is
where I think I led them astray).

The answers indicate that the powdered baking soda reacted
faster.  One student said that the reaction was just a fast in both
but the powdered baking soda generated carbon dioxide faster.  I now
think this student may be correct.

This has me thinking that "faster" is confusing between spent
reactants and the amount of time to react.

And then I confused myself.  Here are the questions I am struggling with:
Are all chemical reactions, on the molecular level at the same rate
of speed, or do they differ?  If yes, that seems unusual in
nature.  If no, what determines the rate of reaction (not time to
reaction completion of available reactants)?
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Hi Justin,

In the case of your baking soda experiment, with all other factors 
being equal, the speed of the reaction of the baking soda with 
vinegar would be the same for both forms.  As you were trying to 
teach, the powdered baking soda has more sites for the reaction to 
take place simultaneously.  Thus, overall all of the powdered baking 
soda will react before the peletized form.

Chemical reactions however do not happen at the same speed.  Other 
factors such as temperature, pH, etc. can have a tremendous affect 
on reaction speed.  For instance, the reduction of Cr+6 to Cr+3 can 
take hours at pH 8, if the pH is <2, the reaction occurs in seconds.

The powdered baking soda generated carbon dioxide at the same rate 
as the peletized form per equal moles of baking soda reacting. More 
moles react and generate more CO2

Bob Hartwell
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Justin,

Think of the rate of reaction (at the molecular level) as being 
dependent on two things: a spatial factor (rate of collisions in the 
correct orientation) and energy. You can see this mathematically in 
the Arrhenius equation (where the spatial factor is sometimes split 
between rate of collisions and orientation).

This means that at the molecular level, if you can increase the rate 
of collisions (and presumably the collisions that are in the correct 
orientation), then the over-all rate of the reaction will speed up. 
Thus, if you take the same amount of substance, but have one in 
powder form and another in a compact lump, then the rate of reaction 
of the powder will be faster (more surface to volume, more 
collisions). You can see this if you react an antacid tablet with 
vinegar (no stirring, do not wait for it to completely dissolve) as 
opposed to the same antacid tablet ground really fine. This is also 
why coal mines are dangerous (because of the fine dust in the air), 
but charcoal is safe enough to cook with.

There are many macroscopic factors/actions that affect rate of 
collisions: stirring, solubility, concentration, particle size, etc. 
- and this might have been the source of the confusion. But if all 
of these are controlled, then the rate of reaction (molecular level) 
should be reflected in the total time of reaction completion.

Also at the molecular level, the rate of reaction will speed up if 
energy is supplied. Thus, most reaction should go faster if they are heated.

With regard to your particular experiment, the reaction of sodium 
hydrogen carbonate (baking soda) with acid (vinegar) is a very fast 
reaction in the first place, so you really have to be careful that 
you are mindful of factors that affect rate to see a difference. But 
it should work for you. I suspect that the students who thought that 
the reaction was just as fast in both cases might have ignored the 
time it took for the pellet to dissolve, or may not have been using 
the same amount of liquid. The other possibility is that the vinegar 
was the limiting reagent and could have been controlling the over-all speed.

Hope this helped.

Greg (Roberto Gregorius)
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I am not quite sure what a "speed of reaction" means to you.  Your 
students may not know what it means to you either, which will make 
it difficult for any of us to communicate.  So I will begin by 
defining what it means to ME, and go from there.

Like any rate, a reaction rate is a change in something with 
time.  Specifically, the rate of a chemical reaction is the time 
derivative of the concentration of the product species (actually, of 
the concentration raised to the power of its stoichiometric 
coefficient).  In other words, for a reaction, say,
   A -> B,
the reaction rate is defined as
  rate = d[B]/dt,
where [B] is the concentration of the product species B.
If a reaction creates some different number of molecules of B, say, two, as in
   D -> 2B,
the reaction rate is
   rate = d([B]^2)/dt,
where [B]^2 means the square of [B].

Many reactions change their rates as they proceed.  Often the rate 
depends on the concentration of the starting materials; as these are 
depleted, the reaction rate drops.  Sometimes reactions are 
autocatalytic, which means that the product accelerates the 
reaction: the rates of such reactions skyrocket after a little 
product is formed.  Other reactions generate heat, which raises the 
temperature and accelerates the reaction.  Many different things can happen!

Now, it is hard to measure a reaction rate directly.  Usually what 
you can measure is the amount or concentration of one of the 
starting materials or products, and you need to estimate what the 
rate of its change is.  If you can measure the change over some time 
interval, you can calculate the average reaction rate over that interval, as
   average rate = (change in [B])/(elapsed time).

With your powdered baking soda, you and your students saw that 
powdered baking soda generated gas faster than the same mass of 
baking soda in tablet form.  What is the reaction whose rate you are 
trying to assess?  If the reaction is the generation of gas, then 
the system giving the faster gas generation is the system with the faster rate.

I do not think this actually answered your question because I do not 
believe I understand what it is you want to know.  I hope this can 
give you a beginning, so that you can ask again in the hope that we 
can communicate more efficiently once we understand each other better.

Richard Barrans
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