Transcript Big Numbers mean Big Problems

Big Numbers mean Big Problems
We can picture 20 sheep, cars, … in our minds.
How
about large numbers?
Number of molecules – defined in terms of
Avagadro’s number
Na=6.022 136 7(36) x 1023 molecules/mole
How big is this number?
Consider standing on the shore of a small lake
~5 mi x 1 mi x 20 ft deep
Standing looking across the lake
Houses look about 1/2 inch high
Cars are too small to see
Take 1 Aramark sugar packet
pour it into the lake – stir and wait until mixed
Fill a 1-liter mug with pond water - drink
How many sugar molecules are in the mug?
How do we solve the problem?
Avagadro’s number tells us how many molecules
there are in a mole.
How many molecules did we put into the lake?
What is the volume of the lake?
We know the volume of the mug.
We need a concentration.
Avagadro’s number
A gram molecular weight of a
substance (a mole) contains
Avagadro’s number of molecules.
Periodic Table
of the Elements
Sugar – C12H22O11
From periodic table
mass
C = 12.01 g/mol
H = 1.008 g/mol
O = 16.00 g/mol
Mass of a mole of sugar
 12.01 g 
 1.008 g 
12 C atoms 
  22 H atoms 

 mol C atoms 
 mol H atoms 
 16.00 g 
11 O atoms 

 mol O atoms 
= 342.296 g/mol sugar = 342 g/mol
gram molecular weight
How much sugar (in moles) did we add to the
lake?
Weigh a packet of sugar – 2.8055 g
Probably only good to 2 significant figures –
2.8 g
2.8 g sugar
# mol sugar 
342 g sugar / mol sugar
 0.008 19 mol sugar
What is the volume of the lake?
US miles, feet !!! We need to convert to SI
1 mi = 5280 ft =1.609 km=1609 m
w
l
d
1609 m 
1609 m 
0.3047 m 


Vlake  1 mi
 5 mi
 20 ft
mi 
mi 
ft


Vlake=78 892 265 m3
We need to find the concentration of sugar in
the water.
A standard unit of concentration is
molarity.
molarity = mol/liter
Lets convert the lake volume to liters.
Vlake
 1
 100 cm 
 78 892 265 m 

3 
 1000 cm  m 
3
Vlake  7.889 10 liter
10
3
Concentration of sugar in the lake from the
Aramark sugar packet
sugar 
0.008 19 mol sugar
10
7.889  10
sugar  1.038  10
13 mol

liter
 1.038  10
13
M
How many molecules are there
in the liter mug?

13 mol  
23 molecules 
# molecules  1.038  10
 1   6.022  10

  
mol 

Concentration
Avagadro’s
number
Volume
of mug
# molecules in mug  6.247  1010 molecules
10
10
 6  10 molecules  10 molecules
1010 = 10,000,000,000
still a fantastically large number
What does this tell you about even small chemical spills,
releases of gases, liquids, and solids into the environment?
How many molecules are we adding?
How many can we tolerate?
Volume of the Gulf of Mexico = 2,434,000km3
Volume of the Deep Horizon oil spill = 780,000m3 = 0.00078km3