Question

A typical sugar cube has an edge length of 1.00 cm. Imagine you have a cubical box that contains a mole of sugar cubes, perfectly packed. What is the edge length of the box in meters? You may assume that the box is made of very thin material so that the inside and outside dimensions are essentially the same. (1 mol = 6.02×1023.)

Answer 1

844368.7 m

Explanation:

We are given that a typical sugar cube has an edge length of 1.00 cm.

We have to find the edge length of the box in meters.

Edge length of sugar cube=1 cm =
`10^(-2)m` (
`1 cm=(1)/(100)m`)

Volume of a sugar cube=
`side* side\time side=(10^(-2))^3=10^(-6)m^3`

1 mole of sugar=
`6.02* 10^(23)units`

Volume of 1 unit=
`10^(-6) m^3`

Volume of
`6.02* 10^(23)` units=
`6.02*10^(23)* 10^(-6)=6.02* 10^(17) m^3`

Volume of box=1 mole of sugar=
`6.02* 10^(17) m^3`

Edge length of box=
`\sqrt[3]{6.02* 10^(17)}=844368.7 m`