Question

In: Chemistry

Suppose you have Avogadro's number of mini marshmallows and use them to cover the state of...

Suppose you have Avogadro's number of mini marshmallows and use them to cover the state of Michigan which has a land area of 5.680 × 104 mi2. Each mini marshmallow has a diameter of 0.635 cm and a height of 2.54 cm. Assuming the marshmallows are packed together so there is no space between them, to what height above the surface, in kilometers, will the mini marshmallows extend?

Solutions

Expert Solution

lets calculate area of Michigan in meter2

1609.34 m = 1 mile

1 mile2 = 2589975.23 m2

5.680 x 104 mi2 = 5.680 x 104 x 2589975.23 m2 = 1.47 x 1011 m2

area of 1 marshmallow = pid2/4 = 3.14 x (0.00635 m)2 = 3.16 x 10-5 m2

assumed no. gap , total marshmallow needed to cover =1.47 x 1011 m2 / 3.16 x 10-5 m2

= 4.65 x1015 marshmallows

this is 1 layer and having height = 2.54 cm

and we have avogadro's no marshmallow = 6.023 x 1023

6.023 x 1023 = n x4.65 x1015

n represents no. of layers

n = 1.29 x 108 layers

1 layer = 2.54 cm

1.29 x 108 layers = 2.54 cm x 1.29 x 108 cm = 3.27 x 108 cm = 3.27 x 103 KM !!

we have to use it all !!!

6.023 x 1023 -


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