How Big Is a Molecule

1
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.

Heres a model of a typical soap molecule
How long??? andHow many in a tiny drop?
2
The Demo
Soap measure how much
Water with pepper On surface
Soap forms a layer one molecule thick on the
water surface
How Long ?
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3
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 figsWhy?
• We used 1.00 microliters (?L) of soap
• How many ?L are in a mL ? Why do I want this in
  mL units?
• That is 0.00100 mL (or cm3)
• The volume of a cylinder is
• V ?r2h h V/?r2
• Why should we be careful about how many digits we
  use in ? ?

4
The Calculations

• 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) 42.926 cm

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
• 0.00100 mL

• Are you comfortable representing such a small
  volume
• in standard notation above? Well, maybe.
  Just wait

5
The Calculations

• Finally, the height of the cylinder, i.e., the
  length of the molecule
• RECALL h V/?r2
• h (0.00100 cm3)/? (42.9 cm)2

volume
area
Unit analysis volume/area length
h 0.000000173 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 10-7 cm

• This is tiny. Youd have to
• stack about 55,000 (5.5 x 104) of them end to
  end
• to equal the thickness of 1 sheet of copy paper.
• lay 945,000,000,000 (9.45 x 1011) of them end to
  end
• to equal a mile

6
Prefix to Prefix conversions

• ?L to mL What do we already know?
• 106 ?L 1 L 103 mL 1 L

We can make a new conversion from what we know
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