STEM ED/CHM Nanotechnology
Surface Area to Volume Ratios of Crystals
Introduction
Ordered, cubic crystals of sodium chloride form as shown if water slowly
evaporates from a solution of table salt. If water evaporates more rapidly, sodium
ions (Na+1) and chloride ions (Cl-1) assemble into less ordered structures.
Goals:
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Form very small cubic crystals by evaporating water from a solution of
sodium chloride.
Compare the Surface Area to Volume Ratio (SA/V ratio) of different sized
crystals.
Use dimensions expressed in scientific notation to compare the crystals you
grow with crystals that have nanoscale dimensions.
The Materials
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Watch glasses or shallow curved glass dish
Table salt
Warming tray or hot plate
Step One: Make or obtain a solution of sodium chloride.
Step Two: Form Sodium Chloride crystals.
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Pour some of the saturate solution into two “watch glasses” or dishes with a
slightly concave surface until approximately half of the area of the dish is
full.
Put the dishes in a location where the water can slowly evaporate. You can
also heat the 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.
Store crystals in a petri dish with a cover.
Determine the Dimensions of Sodium Chloride Crystals
The following procedure can be used to determine the dimensions of a small
crystal of sodium chloride.
 Construct (or be given) 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
Use a calculator to calculate the total surface area of each crustal (in cm2)
Use a calculator to calculate the volume of each crystal (in cm3)
Calculate the Surface Area to Volume Ratio.
You can also use on-line Surface Area to Volume Ratio calculator at:
http://www.cod.edu/people/faculty/chenpe/sa-ratio.html
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).
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 cubic crystal has 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?