In chemistry class today, we were presented the problem of finding the mass and volume of a single grain of very, very fine sand. We are familiar with the concepts of water displacement, etc, but it seems that a grain of sand is just too fine to use these. techniques on. If anybody has any suggestions on how to go about finding these two figures using college chemistry equipment, please share them. Thanks.
Well, if your equipment is not sensitive enough, will they accept an average value?
You could count out a hundred (or thousand) grains and then weigh them and measure their displacement. Divide the measurements by the number of grains and, voila, you have the average size and weight.
The easiest way I can think to do it is find the density of your sand and then determine a size by means of an optical projection method. The best one is probably to prepare a slide of the uniform sample (I’m assuming the sand is uniform) and look at it under a microscope. Measure the diameter of the image of a single grain (perhaps by counting how many grains fit in the view). Then using the laws of magnification you can measure the diameter of a single grain. Assume a spherical grain to determine the volume. You have the density… you have the mass.
Counting the grains out is probably NOT feasible.
Mass is an easy thing to determine using a very sensitive balance or statistically weighting a known large number of particles and averaging them.
Now the volume of that particle is another matter. And the answer will depend on whether you are in high school or in an advanced engineering class.
If you are in highschool the methods given by princeton or pop are good enough.
But if you are in an advanced engineering class you will need some advanced methods because water will not enter the pores inside the grain of sand (so the volume displaced will be wrong). Similarly, the microscope will not look inside the particle (or account of non spherical nature) and hence will give you the wrong volume.
The surface area (and volume of particles) is very important in catalysis and are determined typically using the Brunauer, Emmett and Teller (BET) method. Also used are methods where Mercury and Nitrogen are used in somewhat the manner of water displacement.
Have you ever actually tried to weigh a small object like a protein crystal or a grain of sand ? Electrobalances with microgram sensitivity are very finicky machines.