Ice Under Pressure: Density Changes at 0-14k psi?

[BasketDaN]

From looking at the ice phase diagram (btw, does anybody have a high quality version of this? the one I looked at isn't that great), it appears that ice will remain in its first phase at pressures ranging from 0-14k psi. So if there is water in a container that is capable of resisting 15k psi with no flexing, the ice that will form will be ice II, correct? However, if there is about 13k psi acting on the water (lets say it is in a balloon and the outside air pressure is 13k psi), will the ice that is formed from this freezing water still have a density of .92? In other words what I'm asking is: does the density of ice near the borderline of its first and second phases change gradually (with constant temperature -20 celsius), or is there a sudden change in the molecular structure of the ice at a specific pressure that will very quickly make the density change? Will ice remain at a density of .92 from 0 all the way to 13k psi?

 

[Bystander]

(snip)what I'm asking is: does the density of ice near the borderline of its first and second phases change gradually (with constant temperature -20 celsius), or is there a sudden change in the molecular structure of the ice at a specific pressure that will very quickly make the density change?

Phases in thermodynamics are states of aggregation. They are distinguished by discontinuities in various state functions (properties) describing them. Densities of condensed phases at equilibrium are generally different (ice and water at 273.16 K, near 0 P; 273.15 K , 100 kPa), and solid phases may be kinetically slow transforming (diamond to graphite --- don't count on it), but aren't otherwise special in this regard.

 

[BasketDaN]

Not sure if I completely understood that response, but basically you aren't sure if the density of ice will still be .92 (normal ice density) at 13k psi (very shortly before the point where the pressure on it would classify it as ice II which is 1.02 density I believe)? Thanks for the response.

 

[Bystander]

Not sure if I completely understood that response, but basically you aren't sure if the density of ice will still be .92 (normal ice density) at 13k psi (very shortly before the point where the pressure on it would classify it as ice II which is 1.02 density I believe)? Thanks for the response.

Basically, I'm "very sure" that there is a discontinuity in density at the phase boundary. You are confusing compressibilities of phases with phase change. Ice will not have a constant density, 0.92, over the pressure range 0 to 13kpsi --- it, like everything else in the universe, is compressible, and its density will increase (there are a few odd items that have been observed to expand as pressure increases). Your question, is whether that increase over the pressure range is such that density is a continuous function? If so, the answer is NO.

 

[BasketDaN]

You are confusing compressibilities of phases with phase change.

The ice phase diagram shows that at -20 celsius, ice will go from Ic to II at 14k psi (approx). When I looked up the difference in these phases of ice, I found that ice II is more dense than ice Ic. I think it also said that the molecular structure was different. Because of this, I assumed that the change in density was due to this molecular strucutre alteration; and therefore comparable to h2o phase changes from water to ice; a FAIRLY (yet still changing somewhat with temp) consistent density until a sudden change, right at the 0 celsius mark. But I guess this is not the case with the different phases of ice?

Application: A pipe would have to be much stronger to not burst w/ freezing water inside it if the density of ice remains somewhat consistent up until a sudden point (14k psi is what I've been using) than if the density of ice gradually changes as pressure is increased, right?

 

[Bystander]

Let's back up a couple steps --- be certain everyone's on the same page --- are you familiar with the phase rule, f = c - p + 2 ?

 

[BasketDaN]

Nope, wasn't familiar with that.

Thanks for sticking with me on this... my admittance into MIT depends on a project I'm doing with these concepts working.

 

[Bystander]

Ok --- thought not. Wandering around a phase diagram without the thermo behind the construction of phase diagrams ain't always terribly illuminating.

Short (incomplete) definitions: "phase" --- a homogeneous aggregation of bulk matter; "equilibrium" --- nothing happening, no change, stasis, ---; "state function/variable" --- a quantity or property that depends only upon the state of the system, e.g., T, P, V, ρ, G, H, A, γ C_x, E, H, you get the picture; "chemical potential" --- activity, fugacity, molal Gibbs free energy, a measure of a material's tendency to react (or change phases); "component" --- a chemically pure element or compound making up all or part of a system, or a phase within a system; "composition" --- a quantitative description of the makeup of a system in terms of mole fraction or other composition variable (molarity, molality, demality, normality, ----).

Gibbs (or Gibbs', depending on writing styles) phase rule, f = c - p + 2, is a summary of human experience (I ain't seen derivations) describing the miinimum number of state functions/variables necessary to fix the state of a system where: "f" is the number of degrees of freedom of the system; "c" is the number of components in the system; and, "p" is the number of phases in the system.

Okay --- we're playing with water at 273 K and lower temperatures; we're far below pressures where uncombined mixtures of H₂ and O₂ are more stable than water (given that results from 5-10 years ago indicating such a phenomena have been confirmed). That means we have a single component system. From the Gibbs phase rule, the number of degrees of freedom, f, = 3 - p. That is, if we are looking at a single phase, we must specify 2 state variables/functions to fix the state of the system --- T and P are the usual "suspects," controllable experimentally; fixing T and P will fix the values of every other thermodynamic property of the single phase for that specific pair of T, P values. Two phases, one degree of freedom, T fixes vapor pressure along the liquid-vapor equilibrium and solid-vapor equilibrium lines. Three phases, zero degrees of freedom, the solid-liquid-vapor "triple point;" we cannot move it by adjusting T, P, or any other variable in a single component system.

'Nuff for the mo' --- wrist cramps --- with me so far?

 

[BasketDaN]

Alrighty I'm with ya

 

[Bystander]

Continuing the tour: one component, water; T = -20 C, constant, your selection; and, I think we'll start in the vapor phase at 1 Pa pressure (call it 0.08 mm Hg, 1.4x10^-4 psi, 10^-5 atm, whatever).

Single phase, 1 component, two specified state functions/variables --- the state of the system is fixed --- density is 10mg/m³.

Now, let's proceed along a path of constant T, and increasing P --- we'll increase P by adding vapor to a constant V (open system), or by reducing the the volume (closed system) --- density increases pretty much in accord with ideal gas behavior. We are looking then at ρ = f(T,P) , until P reaches ca. 100 Pa (0.7 mm, -----), the vapor-solid phase boundary. Addition of vapor, or reduction of volume beyond this point result in no increase in system pressure so long as both phases are present; the densities of the two phases, solid and vapor, are each constant --- the overall density of the "system" (water in whatever phases happen to be present) increases until it reaches that of the denser of the two phases, and we're into another single phase region --- two degrees of freedom.

Now we continue increasing P --- compressibility of ice I is going to be 10-30 ppm/atm, 100-300 ppm/MPa, and we're kicking P up to 100 MPa before running into the I-II boundary --- density of I increases 1-3%. We are now at another two-phase condition --- T, P, and phase densities remain constant until least dense phase is totally collapsed into denser (or, if we're going the other way, denser phase is totally expanded into lower density phase).

This description applies only to the equilibrium situation --- we'll go over the metastability problems if you wish, but for the moment, let's stick to the phase diagram.

Am I making sense to you so far?