The following is a crude but effective method for estimating the order of magnit
ID: 534463 • Letter: T
Question
The following is a crude but effective method for estimating the order of magnitude of Avogadro's number using stearic acit (C_18H_36O_2) shown below. When stearic acid is added to water, its molecules collect at the surface and form a monolayer; that is, the layer is only one molecule thick. The cross-sectional area of each stearic acid molecule has been measured to be 0.21 nm^2. In one experiment it is fond that 1.4 times 10^-5 g of stearic acid is needed to form a monolayer over water in a dish of diameter 20. cm. Based on these measurements, what is Avogadro's number? (Assume the dish is circular) Just like last week, what is important here is your critical thinking process. Think of the steps that would be needed to successfully answer this question. Ultimately, you somehow need to use the measurements given to you in the problem and relate them and their units to Avogadro's number. It is always important to realize that these questions are meant to CHALLENGE you. They are not meant to be super easy. If you work with your peers (via this discussion forum) to get to the answer. The process is what is important, the process is what molds you into a critical, independent thinker. As a starting point: You should probably calculate the surface area of the dish and then calculate how many stearic acid molecules would actually fit in that surface area. Also note they give you the grams of the amount of molecules that would fit in that surface so think how you can relate that mass (unit of grams) to the amount of molecules you calculated.Explanation / Answer
Ans. Step 1: Area (surface) of the dish (circle) = pi(r)2
Radius, r = diameter/ 2 = 20.0 cm / 2 = 10.0 cm = 108 nm ; [1 cm = 107 nm]
Now,
Area of dish, A = 3.1416 (108 nm)2 = 3.1416 x 1016 nm2
Number of stearic acid molecules required to form a monolayer on dish =
Area of dish / area of one stearic acid molecule
= 3.1416 x 1016 nm2 / (0.21 nm2 / molecule)
= 1.496 x1017 molecules
Step 2: Given, Mass of stearic acid sample = 1.4 x 10-5 g
Molar mass of stearic acid (C18H36O2) = 284.48264 g/mol
Moles of stearic acid in 1.4 x 10-5 g sample = Mass/ molar mass
= 1.4 x 10-5 g / (284.48264 g/mol)
= 4.921 x 10-7 mol
Let there are NA particles in Avogadro’s number
Now,
Total molecules of stearic acid = Moles of stearic acid x NA
Or, 1.496 x1017 molecules = 4.921 x 10-7 mol x NA
Or, NA = 1.496 x1017 molecules / 4.921 x 10-7 mol
Or, NA = 3.04 x 1023 molecules/ mol
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