Surface Area to Volume
How does the surface area of a solid affect its rate of
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.
What is important is the ratio of surface area to volume. For a sphere,
A = 4 pi R^2 and
V = 4/3 pi R^3. The ration of surface area to volume is S/V = 3/R. Since
the units for area are different than the units for volume, the value of
this ratio depends on the unit used. This is confusing, but you can see
that as the radius, R, gets smaller, the ratio gets bigger (as R approaches
zero, the ratio goes to infinity).
It may be more enlightening to think about how close the sugar is to the
water. For tiny sugar grains, all the sugar is very close to the water so
only a small amount has to dissolve from any grain before it is all
dissolved. For a very large grain, however, a large amount of the grain has
to dissolve before the sugar at the center of the grain is exposed to the
water. Therefore small grains dissolve more rapidly than large grains.
If you would like a more numerical result, consider this. Take a volume, V,
of sugar and form it into identical spherical grains of radius R. This
would make V/(4/3 pi R^3) grains. The total surface area will then be the
surface area of each times the number of grains:
A = 4 pi r^2 *(V/(4/3 pi R^3)) = 3V/R.
So for a volume of 1 cm^3 of sugar formed into grains of radius 0.1 cm, the
total surface area is
30 cm^2. If the grains have a radius of 0.01 cm, the total surface area is
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
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Update: June 2012