Ask A Scientist Physics Archive

      
name         Leah
status       student
age          14

Question -   How does the surface area of a solid affect its rate
of reaction?
I read that finer sugar grains dissolve more quickly than larger sugar
grains. However, I also read that the larger the surface area is, the
quicker it dissolves.
------------------------

Leah,

Finer sugar grains have a vastly larger surface area than larger chunks.. 
The larger the exposed surface, the faster the dissolution (or reaction 
rate) because the solvent has greater access to the solute.
You can convince yourself of my assertion in the first sentence above by 
considering this little thought experiment: Imagine that you have a cube 
of sugar that measures one inch on each edge. Such a cube would have a 
volume of one cubic inch and a total surface area of six square inches -- 
six faces on the cube, each with an area of one square inch.

If you were to cleave it (parallel to one of its faces) you would expose 
two square inches of new interior surface. Another cleavage would expose 
another two square inches of surface. Uncleaved, the surface area of the 
cube is six square inches. Cleaved one time, the total exposed surface 
area becomes eight square inches. The second cleavage produces a total of 
eight square inches.

As you can see, each time the cube is cleaved parallel to one of its 
faces, the total surface area increases by two square inches. Repeated 
cleavages produce ever-increasing surface area -- all the while, the sum 
of volumes of all the smaller pieces continues to add up to one cubic 
inch. Put another way, cutting or grinding the sugar does not make more 
sugar, but it does increase the exposure to dissolution by increasing the 
surface area of the original amount.

Regards,
ProfHoff 894
=====================================================
The "rule" of thumb is reactions involving solids do occur faster the
greater the surface area. However, things are a lot more complicated than
the "rule" implies.

First consider cubical particles of side length L: V = L^3 and the
surface area is: S = 6*L^2 There are '6' faces on the cube. The
surface to volume ratio is:
S/V= 6*L^2 / L^3 = S/V = 6 / L. So as 'L' gets smaller S/V increases.

Second consider spherical particles: V = 4/3(pi)*R^3 and
S = 4(pi)*R^2 so the surface to volume ratio is: S/V = 3 / R. So the
dependence on the "length" parameter 'L' or
'R' is different.

Third, there is almost always a distribution of particle
sizes, so that has a big effect.

Fourth, the particles are not usually solid
objects, but more like a sponge, with internal voids and channels, so the
"surface area" becomes much larger than one would expect from considering
the particles to be closed solids.

Fifth, there is an even more subtle effect. The surface of a solid does 
not behave chemically the same way the
bulk material does. It is much more reactive. For example, you do not
sually
think of glass being soluble in an acid, but finely divided glass (like
glass wool or silica gel) reacts fairly readily with moderately dilute
sulfuric acid. This is a geometric effect.

Sixth, the surface of a solid is more "chemically" reactive than the bulk, 
in addition to the effect of
geometry. This is because the surface of a solid is chemically "different"
that the bulk material.

Seventh, if you consider a given weight of a powder,
the amount of surface per gram of powder is much greater, the higher the
surface area.
     So the more rapid solution of fine sugar and the quicker fine sugar
dissolves are not contradictory statements because fine sugar has a larger
surface area (or more importantly) a larger surface / volume ratio which
increases the rate of solution (which is just a simple chemical reaction).
     The bottom line is that "surface" area and "surface" chemistry are
very intertwined and complicated effects.

Vince Calder
====================================================
Leah,

     Let me change the wording of your second statement slightly to make
it more clear:

"I also read that the 'greater' the surface area is, the quicker it
dissolves."

     Your two statements about rates of dissolving are saying the same
thing.  For the same amount of material the smaller the grain size is
the greater the surface area and the faster it will dissolve.

     To convince yourself of this consider a piece of hard candy --
assume a lifesaver...  It has some surface area when whole.  Break it in
half.  Now the same amount of material has a smaller grain size and it
has the original surface area PLUS the surface area on each piece where
the break exposed more surface.   Break it again and you expose
additional surface area.  The more times you break it the more surface
area you make.

     As an example, let us take a cube of (any) material 1 cm on a side.
Each side is 1 square cm and there are 6 sides for a total of 6 square
cm of surface area.  Now, cut this up into cubes that are 1 mm (0.1 cm)
on each side.  There are 10 mm in a cm so we end up with 10 X 10 X 10 =
1000 cubes with six sides, each 0.1 cm in each direction.  One side is
0.1 X 0.1 = 0.01 square cm.  Six sides each gives 1000 X 6 X 0.01 = 60
square cm of surface area.

     Most sugar crystals would be much smaller than 0.1 cm on a side.
Extremely fine particles can have incredibly large surface areas in a
small space.  I'm told that activated charcoal has such small particles
that a teaspoon of it can have many square miles of surface area.

Greg Bradburn
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