STEM ED/CHM Nanotechnology
Surface Area to Volume Ratios of Self-Assembled Crystals
If water evaporates slowly from a salt water solution, cubic crystals of sodium
chloride form as shown in the photograph below. If water evaporates more rapidly,
sodium ions (Na+1) and chloride ions (Cl-1) self-assemble into less ordered
structures.
Your Goal: Determine how the size of a crystal affects the relationship between
the total surface area of a crystal and the volume of the crystal.
Begin the Self-Assembly of Sodium Chloride crystals.
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Make a saturated solution of sodium chloride by dissolving as much table salt
in a small amount of water.
Pour some of the saturate solution into an evaporating dish or any dish with a
slightly concave surface.
Put the dish in a location where the water can slowly evaporate. You can also
heat the evaporating dish very gently.
Recover some of the sodium chloride crystals after the water has
completely evaporated. A magnifier can be used to select crystals that have
an approximately regular geometric shape.
Determine the Dimensions of the Sodium Chloride Crystals
The following procedure can be used to determine the dimensions of a small
crystal of sodium chloride.
 Construct a data table to record the length, width, and depth of several
sodium chloride crystals. Include columns for the volume, total surface area,
and the Surface Area to Volume Ratio (SA/V) for each crystal.
 Connect a USB Microscope to a computer.
 Calibrate the USB microscope to determine the relationship between the
dimension of an image of an object on the computer’s monitor and the
dimension of the object on the USB’s viewing platform.
 Record the dimensions (in centimeters) of the sodium chloride crystals you
have collected.
Calculate the Surface Area and Volume of Each Crystal
You can use a calculator to calculate the total surface area of each crustal (in
cm ) and the volume of each crystal (in cm3) or you can use an on-line calculator at:
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http://www.cod.edu/people/faculty/chenpe/sa-ratio.html
Calculate the Surface Area to Volume Ratio for each crystal.
If you used the on-line calculator, you would have noticed that it also calculates
the Surface Area to Volume Ratio for a cuboid (an object with six faces and 3
pairs of parallel opposing sides).
You can also use a calculator to determine the Surface Area to Volume ratio by
dividing the Total Surface Area by the Total Volume for each crystal.
Question 1: What happens to the value for the Surface Area to Volume Ratio as
the size of the crystals decrease?
Question 2: How might a decrease in the value for the Surface Area to Volume
Ratio for salt crystals affect the rate at which salt would dissolve in water?
Question 3: How would you design an experiment to determine how the value for
the Surface Area to Volume Ratio for salt crystals affects the rate at which salt
would dissolve in water?
Question 4: Why would a decrease in the value for the Surface Area to Volume
Ratio for salt crystals affect the rate at which salt would dissolve in water?
Surface Area to Volume Ratios at the Nanometer Scale:
You have been using a centimeter ruler to analyze the Surface Area to Volume
Ratio of salt crystals. A Surface Area to Volume Ratio can also be determined for
a nanoscale structure. As an example, a nanoscale structure may have a width of
4.5 nanometers. 4.5 nanometers is equal to 4.5 x 10-9 meters.
Question 5: How can 4.5 nanometers equal be expressed in centimeters?
Question 6: What would be the Surface Area to Volume Ratio for a cuboid
structure that is 16.5 nanometers wide, 120.0 nanometers long, and 4.5 nanometers
thick? Enter data for that nanoscale structure on the data table. If you use the
on-line calculator, you need to enter values in decimal form.
Questions 7: What can you conclude about the Surface Area to Volume Ratios for
nanoscale structures?