How Big Is a Molecule? Purpose: Demonstrate the use of scientific notation, significant figures, and units by estimating the size of a soap molecule When working and thinking in the size range of molecules, numbers that are both very tiny AND gigantic in magnitude are encountered. There is a convenient way to express these numbers. This demonstration provides a fun way to work with uncommonly big and small numbers while at the same time calibrating your thinking about the dimensions and size scale of the world at the molecular level. How long??? and…How many in a tiny drop? Here’s a model of a typical soap molecule…

The Demo Soap: measure how much Water with pepper On surface Soap forms a layer one molecule thick on the water surface Measure radius How Long ?

The Data Basically, the soap film forms a cylinder shape that is 1 molecule thick. If we can calculate the thickness of the cylinder, then we will know roughly how long the soap molecule is. The radius of the film was 16.9 inches. Note the sig figs…Why? We used 1.00 microliters (  L) of soap How many  L are in a mL ? Why do I want this in mL units?How many  L are in a mL ? Why do I want this in mL units? That is mL (or cm 3 ) The volume of a cylinder is: V =  r 2 h ; h = V/  r 2 Why should we be careful about how many digits we use in  ? Top View of soap filmSide view of soap film Height: 1 molecule “thick” Radius

Convert inches to cm There are EXACTLY 2.54 cm in an inch (Why do we need to be careful about the sig figs used in this conversion factor? Why not use 2.5 ? OR 3 ?) (16.9 inches)( 2.54 cm/1 inch) = cm The Calculations Is this ok ??? Because my calculator says so? We need to ROUND to the correct sig figs Answer: 42.9 cm (the conversion factor does not limit the sig figs to 3 in this case because 2.54 is EXACT by definition) How about the volume? We knew the volume of soap was mL Are you comfortable representing such a small volume in standard notation above? Well, maybe. Just wait…

Finally, the height of the cylinder, i.e., the length of the molecule RECALL : h = V/  r 2 h =( cm 3 )/  (42.9 cm) 2 The Calculations volume area Unit analysis: volume/area = length h = cm Do the sig figs look OK? Which value dictates it? What about all those leading zeros ? Now, do you REALLY want to write all those zeros? Answer: h = 1.73 x cm This is tiny. You’d have to stack about 55,000 (5.5 x 10 4 ) of them end to end to equal the thickness of 1 sheet of copy paper. lay 945,000,000,000 (9.45 x ) of them end to end to equal a mile

“Prefix to Prefix” conversions  L to mL …What do we already know? 10 6  L = 1 L ; 10 3 mL = 1 L 10 6  L 1 L ( ) ( 10 3 mL 1 L )= 1  L mL So… 1.00  L = mL (or cm 3 ) Sig figs ?? We can make a new conversion from what we know… **BACK**