How can water exist in a vacuum of 760 mm Hg?

This is the water's phase diagram. Follow the phase diagram as you read this post

In short

The boiling point of water at 760 mm Hg vacuum is -90 degrees Celsius. However, before the water can boil, it must first pass through its triple point at 755 mm Hg vacuum and 0.01degc [phase diagram]. At 755.5 mm Hg vacuum [0.006 atm] and 0.01 degc, water would reach triple point. All three phases coexist in equilibrium at the triple point. Ice formation would begin at triple point and continue indefinitely until the water phase vanished at a much lower pressure, leaving only ice.

In detail

For easy understanding just imagine that you have some water at ambient temperature and 1 atm pressure. You start reducing the pressure on the water. Now look at the phase diagram. As you reduce the pressure you are on the CA curved line on the phase diagram. Point A is the triple point at 0.006 atm and 0.01 degc. You reach point A. At the triple point all three phases solid, liquid and vapor are in equilibrium. At point A the freezing of ice begins and stays in equilibrium with water on the extended CA line. The extension of AC line is the sublimation line.

Probe it further

Gibbs phase rule

Apply Gibbs phase rule F = C - P +2

F is?the degree of freedom. C is components and P is the number of phases

At triple point

F = 1-3 + 2 = 0

There are no degrees of freedom at the triple point. it is a fixed point

Apply Gibbs phase rule to the CA line and its extension

F = C + P - 2

Here C = 1, P = 2

F = 1

On CA line the degree of freedom is one. You can change the composition of CA line by either changing the pressure or temperature. Remember each line in the phase diagram is an equilibrium line when the two phases are at the lowest Gibbs free energy.

You will break ice-vapor equilibrium on CA line when you reduce pressure further beyond the triple point. There will be the conversion of vapor straight to the ice. Just the opposite of sublimation.

Role of entropy

Entropy is the driving force behind the phase change.

To achieve maximum stability, entropy would push low kinetic energy vapor at such low temperatures to the lowest state of energy, which is solid. Entropy would determine the best location for maximum stability and proceed directly to solid at the lowest energy level. This is the inverse of sublimation, which occurs when a solid converts directly to gas. Deposition is the direct conversion of a gas to a solid.

Because freezing is an exothermic process, the entropy will increase during the process. Entropy increases overall because the heat Q released increases entropy in the surroundings. There is no violation of 2nd law of thermodynamics