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

258 8 Effects of Temperature on Sorption and Diffusion of Solutes and Penetration of Water
5. Using the Arrhenius equations given in Fig. 8.3a for the CM number 1 and 6,
calculate the rate constants k ∗ at 10 ◦ C and 50 ◦ C?
6. Calculate the energy of activation for the species/solute combinations shown in
Fig. 8.3b.
7. Why does ED with ivy leaves increase in the order IAA, bifenox, cholesterol?
8. What is the difference between Do and Po?
9. Water permeance of Citrus CM at 5 and 35 ◦ C is 1.36 × 10 −8 and 1.17 ×
10 −7 m s −1 respectively. For MX, the respective values for Pw is 6.14 × 10 −6
and 3.04 × 10 −5 m s −1 (Fig. 8.7, ascending T ). How much larger is Pw of the
MX at 5 and 35 ◦ C? What are the Arrhenius equations for CM and MX?
10. From the slopes given in Fig. 8.9, ED and EP can be calculated and 10.3 and
36.7kJ mol −1 respectively are obtained. ∆HS = −26.4kJ mol −1 can be calculated
by difference (10.3–36.7) as specified in (8.18). If ∆HS is calculated from
the slope of the plot log Kwv vs 1/T we obtain −30.7kJ mol −1 . How do you
explain this difference between the two ∆HS values?
Solutions
1. K is the slope of a plot internal vs external concentration, while k is obtained
when the logarithms of the two variables are plotted. When n = 1, then
K = k = 90.
2. ∆G = 0.
3. ∆H = T∆S.
4. ∆S = 66kJ mol −1 K −1 .
5. For CM 6, we obtain 3.7 × 10 −8 (10 ◦ C) and 8.2 × 0 −5 s −1 (50 ◦ C) respectively.
For CM 1 we have 4.9 × 10 −9 (10 ◦ C) and 4.61 × 10 −5 s −1 (50 ◦ C). With CM 6
having the initially highest k ∗ , the increase with T was 2,216-fold. With CM 1
the increase was even 9,408-fold. The k ∗ ratio between the two CM is 7.55 at
10 ◦ C and 1.78 at 50 ◦ C.
6. ED is 123.5kJ mol −1 (Hedera/IAA), 162.5kJ mol −1 (Hedera/bifenox), 189.5kJ
mol −1 (Hedera/cholesterol) and 153.4kJ mol −1 (Ilex/bifenox).
7. Because solute size increases from 130, 216 to 349cm 3 mol −1 (Appendix B)
and the activation energy is larger when larger holes must be formed in the
membrane matrix.
8. Eo depends on jump distance within the polymer chains and entropy (8.11). Po
depends in addition on thickness ℓ of the cuticles and on sorption of water in the
polymer and in waxes.
9. The ratio of Pw is 451 at 5 ◦ C and 260 at 35 ◦ C. The Arrhenius equation for CM
is Po = 3.98–6,142 × 1/T, and for the MX Po = 4.44 − 4,571 × 1/T.
10. The individual data points for log Kwv were obtained from individual data of log
D and log Pw at the respective temperatures. The difference is due to rounding
errors.