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When pressure increases, volume decreases. If an extremely high pressure is applied to a liquid, is it possible to reduce it's volume to an extent where the molecules are very tight together, hence becoming a solid? Or do changes in pressure and volume not alter the physical properties of the substance and the liquid remains liquid?

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It is possible to change a liquid into a solid, or in general change the phase a substance finds itself in by just altering the pressure.

You might want to refer to some graphs known as Phase diagrams that portray the effect of temperature and pressure on the physical state of a substance.

phase diagram
(source: purdue.edu)

In this example if you're to draw a straight line from the point B to D, it'll have a subtle positive slope. So there's a possibility to transform a liquid into a solid without making any changes to the temperature conditions.

You might have heard of solid $\ce{CO2}$ or dry ice. I might be wrong but a part of me says carbon dioxide is pressurised and refrigerated for it to form.

An interesting thing to note here is that in case of a gas turning into a liquid, there's a temperature known as Critical Temperature ($T_c$) above which the gas cannot be liquified no matter how much pressure is applied.

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    $\begingroup$ Since the curve from B to D is concave, following the straight line from B to D will never leave the liquid phase. But if you choose a temperature between B and D and change the pressure (i.e. follow a line parallel to the pressure axis), you will see a phase transition (liquid/solid). $\endgroup$ – aventurin Apr 17 '17 at 8:43
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    $\begingroup$ Actually, the phase diagram for water seems to go the other way. $\endgroup$ – Chet Miller Apr 17 '17 at 12:11
  • $\begingroup$ @ChesterMiller Agreed. Phase diagram of water is different from those of other compounds. $\endgroup$ – Berry Holmes Apr 17 '17 at 12:20
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    $\begingroup$ It's only locally different; about 1 GPa would solidify it all right. $\endgroup$ – Mithoron Apr 17 '17 at 14:04

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