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?

Answer 1

Answer:

The stack would be 5.002 × 10⁷ inches high.

Explanation:

1 mole of ice cubes contains 6.022 × 10²³ cubes,

1 ice cube has a volume of 1 in³

This translates to a total volume of 6.022 × 10²³ in³

If we call the height of the stack of ice cubes we're about to produce H

The volume of ice cubes we have will take up a volume of [(3 × 10⁶)mi² × H]

Hence, we convert this area of land to in²

3 × 10⁶ mi² = 1.204 × 10¹⁶ in²

Therefore

6.022 × 10²³ = 1.204 × 10¹⁶ × H

H = (6.022 × 10²³)/(1.204 × 10¹⁶) = 5.002 × 10⁷ inches.