# How to find the volume of ice given its density, and the volume and density of water used? [closed]

Just trying to understand density calculations, for example,

Water has a density of $\pu{0.997 g cm^-3}$ at $\pu{25 ^\circ C}$; ice has a density of $\pu{0.917 g cm^-3}$ at $\pu{-10 ^\circ C}$.

If a soft-drink bottle whose volume is $\pu{2.00 L}$ is completely filled with water and then frozen to $\pu{-10 ^\circ C}$, what volume does the ice occupy?

• – Curt F. Sep 20 '16 at 1:01

It depends.... under steady state conditions

1. If the bottle is glass, then the glass shatters, and the frozen water sublimes so there is no ice left.

2. If the container can withstand the pressure without distorting and the container volume changes less than $\pu{0.005 L}$ with a temperature change from $\pu{25 ^\circ C}$ to $\pu{-10 ^\circ C}$, then the final volume will be $\pu{2.00 L}$.

3. If container was so flimsy so that it distorted at a slight change in atmospheric pressure, and it was initially filled completely ($\pu{2.00 L}$) at $\pu{25 ^\circ C}$; then the ice would occupy a volume of: $$\pu{2.00 L} \cdot \frac{\pu{0.997 g cm^3}}{\pu{0.917 g cm^3}}= \pu{2.17 L}$$

4. If the container distorts, but is pressurized, then the volume will be $$\pu{2.00 L} \le V \le \pu{2.17 L}$$

• Thank you so much! I realize you are probably at Phd level chem but your answer was way over my head, there was only one simple answer and it was 2.17 so thank you. – Atticus283blink Sep 20 '16 at 4:02
• I was trying to be a smart ass. I was not really trying to do your homework. – MaxW Sep 20 '16 at 4:38
• Damn man coulda fooled me but its not hw. Im practicing dimensional analysis. – Atticus283blink Sep 20 '16 at 15:17