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

3.1 Units of Permeability 55
3.1.1 Example
Diffusion of water vapour across a polyethylene terephthalate (PET) membrane of
0.1 cm thickness was measured at 25 ◦ C. The vapour pressure in the donor chamber
was 2.375 cmHg, which is the saturation vapour pressure of water at 25 ◦ C. Jv was
4.2 × 10 −7 cm 3 vapour (STP) per cm 2 and s. From these data PHg can be calculated
using (3.1):
PHg = 4.2 × 10−7 cm 3 (STP) × 0.1cm
cm 2 s × 2.375cmHg
= 1.77 × 10 −8cm3 (STP)cm
cm2 . (3.2)
scmHg
One might be tempted to simplify this dimension of PHg and write cm 2 s −1 , because
in writing PHg driving force was 1 cmHg. This was never done, and we shall stick
to the extended unit found in the literature, which does not use the suffix Hg to
characterise this type of permeability coefficient.
In biology, it is not customary to use fluxes based on vapour volume. Instead,
mass fluxes (mol or kg) are used. Hence, we must convert the volume flux of gases
or vapours (Jv) into mass fluxes (J). The volume of water vapour at STP can be converted
to gram water by considering the vapour as an ideal gas, and this was always
assumed when calculating Jv from experimental flux data expressed in pressure units
(Fig. 3.1). The volume (V) of 1 mol of an ideal gas at STP can be calculated from
the ideal gas law:
V =
n × R × T
p
= 1mol × 8.3143m3 Pa × 273.15K
molK × 101,325Pa
= 0.022414m 3 , (3.3)
where R is the gas constant. One mol of water has a mass of 18 g, and the density of
water vapour (δwv) at STP is
δwv = mass
volume =
18g
22.414× 103 cm3 = 8.03 × 10−4gcm −3
and the mass flux of water (Jw) can be calculated
Jw = Jv × δwv = � 4.2 × 10 −7 cm 3 (STP) cm −2 s −1�� 8.03 × 10 −4 gcm −3�
= 3.37 × 10 −10 gcm −2 s −1 .
(3.4)
(3.5)
Before permeance or permeability can be calculated in SI units, the driving force
must be converted. Yasuda and Stannett (1962) and others used cmHg, and conducted
various experiments with different pressures in the donor. Results are shown
in Fig. 3.2. The volume flux was proportional to pressure in cmHg or to partial
pressure.
In the SI system the driving force is often mass per volume, which is molm −3
or kgm −3 . This is practically always the case with solutes dissolved in water. With
water vapour, partial pressure or activity of water can be used as an alternative. At
this point we decide to use partial pressure as driving force, but we shall deal with