Question

If a soft-drink bottle whose volume is 1.10 L is completely filled with water and then frozen to -10 ∘C, what volume does the ice occupy? Water has a density of 0.997 g/cm3 at 25 ∘C; ice has a density of 0.917 g/cm3 at -10 ∘C.

Answer 1

The ice occupies a volume of 1.196 liters at -10 ºC.

Step-by-step explanation:

We must remember that density (
`\rho`), measured in grams per cubic centimeters, is the ratio of mass (
`m`), measured in grams, to occupied volume (
`V`), measured in cubic centimeters, that is:

`\rho = (m)/(V)`

We clear the mass within the formula:

`m = \rho\cdot V`

The mass of the water inside the soft-drink bottle is: (
`\rho = 0.997\,(g)/(cm^(3))` and
`V = 1100\,cm^(3)`)

`m =\left(0.997\,(g)/(cm^(3)) \right)\cdot (1100\,cm^(3))`

`m = 1096.7\,g`

There are 1096.7 grams of water filling the soft-drink bottle completely.

Then, the water is frozen to -10 ºC and transformed into ice, the volume occupied by the ice which we can deduct from definition of density. That is:

`V = (m)/(\rho)`

The volume occupied by the ice inside the soft-drink bottle is: (
`m = 1096.7\,g` and
`\rho = 0.917\,(g)/(cm^(3))`)

`V = (1096.7\,g)/(0.917\,(g)/(cm^(3)) )`

`V = 1195.965\,cm^(3)\,(1.196\,L)`

The ice occupies a volume of 1.196 liters at -10 ºC.