Comparing Surface Area Comparing Surface Area to Volume Ratiosto Volume Ratios

Rob SnyderJuly 2011

There are opportunities at many grade levels and in many STEM programs to develop a nanoscale perspective with activities that:

• Require very simple materials and procedures.• Meet local, state, and national STEM learning

standards.• Are closely related to existing STEM topics.• Provide hands-on, inquiry-based, investigative

experiences.• Have students become more familiar with

measurements in meters, centimeters, micrometers, nanometers, and picometers.

• Develop skill in calculating volumes and areas of very small structures.

• Analyze the surface area to volume ratios of different sized structures.

A crystal growing activity is an example..

Source: http://www.virtualweberbullet.com/salt.html

What are sources of commercial “table salt”?

Salt Evaporation Processes

Evaporation from salt water is the oldest method of salt production. It is practical in warm climates where evaporation rates exceed precipitation rates for extended periods where there are steady prevailing winds

A large area San Francisco Bay is used for commercial salt production that include household sea salts.

Salt Mines

Some salt deposits formed as water slowly evaporated from ancient shallow seas.

Geologic changes then buried the deposits deep beneath Earth’s surface.

This salt mine is 1200 feet below Detroit.

Source: http://apps.detnews.com/apps/history/index.php?id=17

Salt Domes are also a source of commercial and household grade “salts”.

Salt deposits are found in domes that formed when pressures forced salt up through Earth’s rock layers from depths as great as 30,000 or 40,000 feet.

Large sodium chloride crystals like this come from deposits where sodium and chloride ions slowly formed a crystalline lattice structure,

Crystals of NaCl can show cubic cleavage due to the ratio of diameters of sodium and chloride ions.

r+ = cation radius r- = anion radius

Source: http://wikis.lib.ncsu.edu/index.php/Halite-NaCl

Lithium iodide (also an alkali metal halide) comes closest to adopting a truly close packed cubic crystalline structure.

The Crystal Dimensions ActivityPart One: Today

You will be given a solution of NaCl.

Watch glasses or shallow dishes can be used to evaporate the water from the solution.

Develop a strategy to produce very small, regularly shaped crystals as water evaporates. Hot plates and sunny or shaded spaces are available.

Part Two: The next several days

Monitor and manage the formation of small crystals during the next several days. Hot plates and sunny windowsill are available.

Use a USB microscope to measure and record dimensions of small NaCl crystals as they form and store crystals in a covered Petri dish.

Calculate and Record the Surface Area/Volume Ratios of NaCl crystals.

Surface Area to Volume Ratios

One of the first experiences that students have with a discussion of the relationship between surface area and volume occurs during a study of cell structures and/or the metabolism rates of animals.

How has habitat influenced the surface area/volume ratio of the ears of these two animals?

SA/V ratios influence dissolution rates of solutes.

Dissolution rates also depends on:

• Temperature• Mixing• Degree of

unsaturation

The use of the terms dissolution, dissociation, and solvation varies widely in science textbooks.

A data table can be used to record SA/V Ratios of regularly shaped crystals.

Crystal

Length

(cm)

Width

(cm)

Height

(cm)

Total Surface Area (cm2)

Volume (cm3)

SA/V Ratio

An On-Line Calculator is available at: (http://www.cod.edu/people/faculty/chenpe/sa-ratio.html )

Two comments about units

Changes in SA/V ratios depends on the units used.

The SA/V Ratio is an expression of the number of units of area per unit volume ( e.g. # of cm2 per cm3.)

Part Three: Friday

Discuss what you have discovered about the Surface Area to Volume (SA/V) Ratios of your NaCl crystals.

Compare SA/V Ratios of the NaCl crystals with crystals that have nanoscale dimensions.

An example of a nanoscale crystal

University of Surrey researchers have found a way to make ultra-small pure carbon crystals entirely formed from the spherical carbon ‘buckyball’ molecule known as C60.

Source: http://www.sciencedaily.com/releases/2008/07/080714150657.htm

I micrometer = 1µ = 1 x 10-6 m = 1 x 10-4 cm

What is the SA/V Ratio of the nanocrystal?

• If the length (h) of the cylinder = 0.5 µm = 0.5 x 10-4 cm• If the radius of the end (R) = 0.05 µm = 0.05 x 10-4 cm

What is the SA/V Ratio of the nanocrystal?• Area of Cylinder = 2πR2 + 2πRh• Area = 2π(0.05 x 10-4 cm)2 + 2π (0.05 x 10-4 cm)(0.5 x 10-4 cm)• Area = 1.73 x 10-7 cm2

• Volume = πR2h = π (0.05 x 10-4 cm)2 (0.5 x 10-4 cm)• Volume = 3.925 x 10-12cm3

• SA/V Ratio = 1.73 x 10-7 cm2 ÷ 3.925 x 10-12cm3

• SA/V Ratio = 0.441 x 105

How does this SA/V Ratio compare with those of your NaCl crystals?

Is this simple NaCl crystal a nanoscale structure?

1 picometer (pm) = 1 x 10-12 m = 1 x 10-10 cm

The grey spheres are neutral atoms.

Does the crystal have a nanoscale dimension?

• The length of one edge = 167 + 154 + 167 = 488 pm• 488 pm = 488 x 10-12 m = 4.88 x 10-10 m = 4.88 x 10-8 cm

What is the SA/V Ratio of the simple NaCl crystal?

• Area of one face = (4.88 x 10-8 cm)2 = 2.38 x 10-16 cm2

• Total area = 6 x (2.38 x 10-16 cm2) = 1.428 x 10-15 cm2

• V = L x W x D = (4.88 x 10-8 cm)3 = 1.162 x 10-22 cm3

• SA/V Ratio = 1.428 x 10-15 cm2 ÷ 1.162 x 10-22 cm3

• SA/V Ratio = 1.229 x 107

What are implications of such a high SA/V Ratio?

Summary Questions

• How well does an activity like this develop a nanoscale perspective?

• Where can this type of activity be integrated into your STEM curriculum?

• What skills and perspectives developed during this activity support the study of other STEM topics?