Question

Consider 4.00 mol of liquid water.Imagine the molecules to be, on average, uniformly spaced, with each molecule at the center of a small cube. What is the length of an edge of each small cube if adjacent cubes touch but don't overlap?

Answer 1

`L \approx 3.103* 10^(-10)\,m`

Step-by-step explanation:

The mass of water is:

`m_{H_(2)O} = (4\,mol)\cdot (18\,(g)/(mol) )`

`m_{H_(2)O} = 72\,g`

`V_{H_(2)O} = \frac{72\,g} {1\,(g)/(cm^(3)) }`

`V_{H_(2)O}= 72\,cm^(3)`

According to the Avogadro's Number, there are
`6.022* 10^(23)\,(molecules)/(mol)`. The total number of molecules in the water is:

`n = 2.409* 10^(24)\,molecules`

The volume occupied by a molecule is:

`V_(molecule) = \frac{V_{H_(2)O}}{n}`

`V_(molecule) = (72* 10^(-6)\,m^(3))/(2.409* 10^(24))`

`V_(molecule) = 2.989* 10^(-29)\,m^(3)`

The length of an edge of such cube is:

`L = \sqrt[3]{V_(molecule)}`

`L \approx 3.103* 10^(-10)\,m`