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

1 mile

20 feet

5 miles

Take 1 Aramark sugar packet pour it into the lake – stir and wait until mixedFill a 1-liter mug with pond water - drinkHow many sugar molecules are in the mug?

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.

How do we solve the problem?

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 tablemass C = 12.01 g/mol

H = 1.008 g/molO = 16.00 g/mol

Mass of a mole of sugar

00.16 11

.0081 22

01.12 12

atomsOmol

gatomsO

atomsHmol

gatomsH

atomsCmol

gatomsC

= 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 gProbably only good to 2 significant figures –

2.8 g

sugarmolsugarg

sugargsugarmol

/ 342

8.2 #

sugarmol 19 008.0

What is the volume of the lake?

US miles, feet !!! We need to convert to SI1 mi = 5280 ft =1.609 km=1609 m

ft

mft

mi

mmi

mi

mmiVlake

3047.0 20

1609 5

1609 1

w l d

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.

3

33 100

1000

1 265 892 78

m

cm

cmmVlake

literVlake 10 889.7 10

Concentration of sugar in the lake from the Aramark sugar packet

liter

sugarmolsugar

10889.7

19 008.010

Mmol

sugar 1313 10038.110038.1

How many molecules are there in the liter mug?

moleculesmuginmolecules 1010247.6 #

mol

moleculesmolmolecules 2313 10022.6 1 10 038.1#

Volume

of mugAvagadro’s

numberConcentration

moleculesmolecules 1010 10106

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 (This is equal to roughly 3ppb)