The Foundations of Chemistry

decreased to, say, 234 torr at point H.If we wished to hold the pressure at 234 torr and

condense some of the vapor, it would be necessary to cool the vapor to 70°C, point I,

which lies on the vapor pressure curve, AC.To state this in another way, the vapor pres-

sure of water at 70°C is 234 torr.

Suppose we move back to solid at point E(355 torr and 10°C). If we now hold the

temperature at 10°C and reduce the pressure, we move vertically down along EJ.At a

pressure of 2.1 torr we reach the sublimation curve, at which point the solid passes directly

into the gas phase (sublimes) until all the ice has sublimed. An important application of

this phenomenon is in the freeze-drying of foods. In this process a water-containing food

is cooled below the freezing point of water to form ice, which is then removed as a vapor

by decreasing the pressure.

Let us clarify the nature of the fluid phases (liquid and gas) and of the critical point by

describing two different ways that a gas can be liquefied. A sample at point Win the phase

diagram of Figure 13-18b is in the vapor (gas) phase, below its critical temperature.

Suppose we compress the sample at constant Tfrom point Wto point Z.We can iden-

tify a definite pressure (the intersection of line WZwith the vapor pressure curve AC)

where the transition from gas to liquid takes place. If we go aroundthe critical point by

the path WXYZ,however, no such clear-cut transition takes place. By this second path,

the density and other properties of the sample vary in a continuous manner; there is no

definite point at which we can say that the sample changes from gas to liquid.

A weighted wire cuts through a

block of ice. The ice melts under the

high pressure of the wire, and then

refreezes behind the wire.

A fluid belowits critical temperature

may properly be identified as a

liquid or as a gas. Abovethe critical

temperature, we should use the term

“fluid.”

–10 0.01 70 80 374

2.1

4.6

355

218 atm

G

H

B C

E

Solid

A

J

D

Gas

F

Liquid

Temperature (°C)

Pressure (torr)

(a)

I

TC

A

Solid

Gas

Liquid

ZY

W X

PC C

(b)

P

T

Figure 13-18 Some interpretations of phase diagrams. (a) The phase diagram of water.

Phase relationships at various points in this diagram are described in the text. (b) Two paths

by which a gas can be liquefied. (1) Below the critical temperature. Compressing the sample

at constanttemperature is represented by the vertical line WZ. Where this line crosses the

vapor pressure curve AC,the gas liquefies; at that set of conditions, two distinct phases,gas

and liquid, are present in equilibrium with each other. These two phases have different

properties, for example, different densities. Raising the pressure further results in a

completely liquid sample at point Z. (2) Above the critical temperature. Suppose that we

instead first warm the gas at constant pressure from Wto X,a temperature above its critical

temperature. Then, holding the temperature constant, we increase the pressure to point Y.

Along this path, the sample increases smoothlyin density, with no sharp transition between

phases. From Y,we then decrease the temperature to reach final point Z,where the sample

is clearly a liquid.