Water and Solute Permeability of Plant Cuticles: Measurement and ...

56 3 Permeance, Diffusion and Partition Coefficients: Units and Their Conversion
J v (cm 3 (STP) cm −2 s −1 )
4e-7
3e-7
2e-7
1e-7
Vapour pressure of donor (cm Hg)
0 0.48 0.95 1.43 1.90 2.375
5e-7
slope: 4.2 x 10 −7 cm 3 (STP)/cm 2 s
0
0.0 0.2 0.4 0.6 0.8 1.0
Partial pressure of donor
Fig. 3.2 Volume flux of water vapour across a polyethylene terephthalate (PET) membrane [Jv
(STP) plotted vs partial pressure of donor (p/p0)]. Membrane thickness was 1 mm and temperature
25 ◦ C. (Redrawn from Yasuda and Stannett 1962)
other driving forces in more detail later. Since water activity of the vapour is equal
to partial or fractional vapour pressure (p/p0), that is awv = p/p0, we can convert
driving force in cmHg to partial pressure simply by dividing actual vapour pressure
by saturation vapour pressure. With water at 25 ◦ C, saturation vapour pressure is
2.375 cmHg.
Based on the CGS system of the original literature, permeability (Pw) of a 1 cm
thick membrane is
Pw = Jw ×ℓ
aw
= 3.37 × 10−10 g(0.1cm)
cm 2 s × 1
4.0
2.4
3.2
1.6
0.8
= 3.37 × 10 −11 gcm −1 s −1
0
J W X10 10 g cm −2 s −1
(3.6)
and since 1 g of water at 25 ◦ C has a volume of 1cm 3 , Pw is 3.37 × 10 −11 cm 2 s −1
or 3.37 × 10 −15 m 2 s −1 . In this calculation the water flux enters as mass (g) and is
converted to volume of liquid water. The driving force is water activity (or partial
vapour pressure). With pure water as donor, Pw can be calculated by dividing
(Jw ×ℓ) by the water concentration (Cw), which at 25 ◦ C is 1gcm −3 or 1,000kgm −3 .
Cw depends much less on temperature than Cwv. For a solvent, a = γN where γ is
the activity coefficient and N is the mol fraction. Considering water as pure ideal
solvent, both γ and N are 1.0, and we have Cw = aw. Hence, Pw is numerically
identical when driving forces are either Cw, awv or p/p0.
In a closed system, equilibrium between vapour and liquid water is established.
By definition pure water has an activity of 1.0, and water activity is numerically