Question

The number of objects in a mole is so fantastically large as to be incomprehensible from everyday experience. If a mole of ice cubes (each 1 in^3) were stacked neatly edge to edge over the entire continental United States (area = 3.0 x 10^6 mi^2), how high would the stack be?
[Assume the land is flat.]

Answer 1

We know that 1 mi=63360 in

So area of the entire continental US (in²)=3.0 x 10⁶ mi² x (63360 in/mi)²

=12043468800 x 10⁶ in²

Surface area of 1 cube=1 in x 1 in=1 in²

Number of cubes on the surface=surface are of the entire continental US (in)/surface are of 1 cube (in²)

=12043468800 x 10⁶ in²/1 in²

=12043468800 x 10⁶

Volume of 1 ice cube=1 in³

Number of ice cubes in 1 mol=6.02 x 10²³

Volume of 1 mol ice cubes=6.02 x 10²³ cubes x 1 in³/cube

=6.02 x 10²³ in³

As the ice cubes are stacked edge to edge, the resulting shape after placing them on the surface would be cuboidal whose volume is given as length x width x height. The length x width means the surface area of the entire continental US over which these are placed.

Assuming the height of stack as h

Volume of 1 mol ice cubes=Surface area of the entire continental US (in) x h

6.02 x 10²³ in³=12043468800 x 10⁶ in² x h

So h=6.02 x 10²³ in³/12043468800 x 10⁶ in²

=49985598.83 in

So the height of the stack=49985598.83 in