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Comparing Surface Area to Volume Ratios Rob Snyder July 2011

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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.

What are sources of commercial “table salt”?

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

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.

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 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.

Crystals of NaCl can show cubic cleavage due to the ratio of diameters of sodium and chloride ions.r+ = cation radius r- = anion radius

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

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

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.

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.

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.

Dissolution rates also depends on:

Temperature

Mixing

Degree of unsaturation

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

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.)

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.

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.

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

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

- 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?

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

The grey spheres are neutral atoms.

- 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?

- 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?