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

Answer:

844368.7 m

Step-by-step 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 =$10^{-2}m$ ($1 cm=\frac{1}{100}m$)

Volume of a sugar cube=$side\times side\time side=(10^{-2})^3=10^{-6}m^3$

1 mole of sugar=$6.02\times 10^{23}units$

Volume of 1 unit=$10^{-6} m^3$

Volume of $6.02\times 10^{23}$ units=$6.02\times10^{23}\times 10^{-6}=6.02\times 10^{17} m^3$

Volume of box=1 mole of sugar=$6.02\times 10^{17} m^3$

Edge length of box=$\sqrt[3]{6.02\times 10^{17}}=844368.7 m$