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How Big Is a Molecule?. Purpose : Demonstrate the use of scientific notation, significant figures, and units by estimating the size of a soap molecule

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how big is a molecule

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.

Here’s a model of a typical soap molecule…

How long???

and…How many in a tiny drop?

the demo

Measure radius

The Demo

Soap: measure how much

Water with pepper

On surface

Soap forms a

layer one molecule

thick on the water

surface

How

Long ?

http://www.ksvltd.com/pix/keywords_html_278c1fa4.jpg

the data

Top View of soap film

Side view of soap film

Radius

Height: 1 molecule “thick”

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?
  • 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  ?
slide4

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…
the calculations
The Calculations

volume

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

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. You’d 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
prefix to prefix conversions

10-3 mL

1 L

103 mL

)

)

=

(

(

1 L

106L

1 L

So…

1.00 L = 0.00100 mL (or cm3)

Sig figs ??

“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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