Surface Area to Volume ```Name: Leah Status: student Age: 14 Location: N/A Country: N/A Date: 8/13/2004 ``` 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. Replies: 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 300 cm^2 Best, Dick Plano, Professor of Physics emeritus, Rutgers University Click here to return to the Physics Archives

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