### Re: A mole of M&M's would fill how many holes the size of Lake Erie?

Date: Wed Feb 6 16:51:41 2002
Area of science: Chemistry
ID: 1012959678.Ch
Message:

Since I've already done similar calculations on moles of salt, sugar, water, and horses (yes, horses), I couldn't pass up this latest twist, especially since it has some interesting calculations and results. First, we need to know the volume of an M&M™ candy (milk chocolate: no peanut, peanutbutter, or crispy): I was going to figure this out myself by purchasing a bag of M&Ms from the bookstore downstairs, and then measuring their displacement with a graduated cylinder, but then I found Bernie Tao's "M&Ms contained in an Erlenmeyer Klein Flask" site. According to Bernie Tao's calculations, the volume of a single M&M candy is 0.45239 cc (cubic centimeters). While you weren't originally interested in the void volume of the M&Ms, he has already calculated this for M&Ms packed in a Hexagonal Close Packed (HCP) arrangement and determined this to be 40.31% of the total space; i.e., if the void volume is 40.31%, then the M&Ms should take up 59.69% of the available space. Next, we need the volume of Lake Erie - you gave a volume of 483 km3, which exactly agrees with the Lake Erie Facts and Figures pages. Now, on to the calculations:

```483 km3 = 483 x 109 m3 = 483 x 1015 cc

Divided by the volume of an M&M adjusting for void volume, and

In HCP: 637 x 1015 M&Ms per Lake Erie (6.37 x 1017)

Compressed (i.e. no void volume):  1069 x 1015 M&Ms (1.07 x 1018)

6.02 x 1023 / 1.07 x 1018 = 5.63 x 105

6.02 x 1023 / 6.37 x 1017 = 9.45 x 105
```

So, if one were to simply empty Lake Erie of water, flora, and fauna, and then fill it with M&Ms (don't eat the ones in the silt - yech!), it would take 945,000 holes the size of Lake Erie to hold a "mole" of M&Ms, or one hole the size of Lake Erie would contain 1.06 micromoles (µM) of M&Ms. (We use micromolar concentrations a lot in the lab, so I'll have to remember this one for incoming students.) If, on the other hand, one were to first purée the M&Ms and then fill an emptied Lake Erie, it would only take a measly 563,000 holes the size of Lake Erie to hold a mole of M&M purée (not as appetizing, but easier to walk across).

Since those are still some pretty large numbers, I decided to use what was left of the mole of M&Ms after filling Lake Erie, and see what else I could fill. None of the world's lakes were much better at holding a mole of M&Ms, so I turned to the oceans. According to various sources, the volume of earth's oceans is around 1.35 billion (thousand million) km3:

```1.35 x 109 km3 = 1.35 x 1024 cc

in HCP: 1.78 x 1024 M&Ms to fill the world's oceans
(I decided against the purée)

1.78 x 1024 / 6.02 x 1023 = 2.96

Or, if you prefer:
```

# It would take about 3 moles of M&Ms to completely fill the oceans of the world.

(An equivalent amount of water would fill about two ounces - a quarter cup.)

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