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17 March, 23:55

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?

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  1. 18 March, 00:06
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    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.
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