Presentation on theme: "Comparing Surface Area to Volume Ratios Rob Snyder July 2011"— Presentation transcript:
1Comparing Surface Area to Volume Ratios Rob Snyder July 2011
2There 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.
3A crystal growing activity is an example. . What are sources of commercial “table salt”?Source:
4Salt 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 windsA large area San Francisco Bay is used for commercial salt production that include household sea salts.
5Salt Mines This salt mine is 1200 feet below Detroit. 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:
6Salt 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.
7Large sodium chloride crystals like this come from deposits where sodium and chloride ions slowly formed a crystalline lattice structure,
8Source: http://wikis.lib.ncsu.edu/index.php/Halite-NaCl Crystals of NaCl can show cubic cleavage due to the ratio of diameters of sodium and chloride ions. r+ = cation radius r- = anion radiusLithium iodide (also an alkali metal halide) comes closest to adopting a truly close packed cubic crystalline structure.Source:
9The Crystal Dimensions Activity Part 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.
10Part 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.
11Surface 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.
12How has habitat influenced the surface area/volume ratio of the ears of these two animals?
13SA/V ratios influence dissolution rates of solutes. Dissolution rates also depends on:TemperatureMixingDegree of unsaturationThe use of the terms dissolution, dissociation, and solvation varies widely in science textbooks.
14Total Surface Area (cm2) A data table can be used to record SA/V Ratios of regularly shaped crystals.CrystalLength(cm)WidthHeightTotal Surface Area (cm2)Volume (cm3)SA/V Ratio
15An On-Line Calculator is available at: (http://www. cod
16Two 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.)
17Part Three: FridayDiscuss 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.
18An 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.I micrometer = 1µ = 1 x 10-6 m = 1 x 10-4 cmSource:
19What is the SA/V Ratio of the nanocrystal? If the length (h) of the cylinder = 0.5 µm = 0.5 x 10-4 cmIf the radius of the end (R) = 0.05 µm = 0.05 x 10-4 cmWhat is the SA/V Ratio of the nanocrystal?Area of Cylinder = 2πR2 + 2πRhArea = 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 cm2Volume = πR2h = π (0.05 x 10-4 cm)2 (0.5 x 10-4 cm)Volume = x 10-12cm3SA/V Ratio = 1.73 x 10-7 cm2 ÷ x 10-12cm3SA/V Ratio = x 105How does this SA/V Ratio compare with those of your NaCl crystals?
20Is this simple NaCl crystal a nanoscale structure? 1 picometer (pm) = 1 x m = 1 x cmThe grey spheres are neutral atoms.
21Does the crystal have a nanoscale dimension? The length of one edge = = 488 pm488 pm = 488 x m = 4.88 x m = 4.88 x 10-8 cmWhat is the SA/V Ratio of the simple NaCl crystal?Area of one face = (4.88 x 10-8 cm)2 = 2.38 x cm2Total area = 6 x (2.38 x cm2) = x cm2V = L x W x D = (4.88 x 10-8 cm)3 = x cm3SA/V Ratio = x cm2 ÷ x cm3SA/V Ratio = x 107What are implications of such a high SA/V Ratio?
22Summary QuestionsHow 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?