10 kN mm−2, vh = 0.10 and vl = 0.13. (It should be noted that, while vh was not obtained experimentally, it has been derived from Betti's condition.) It may be seen that the patterns of inner strains and defl ections from the numerical analysis are similar to their experimental counterparts. Since the Ce linings were segmental, remarks as for the Ch linings may be made regarding the straight longitudinal joint; namely, that, although the bending-moment diagram has a point of infection in the vicinity of the segmental joint, the larger percentage errors exhibited by both Channeline and Celtite linings, relative to the one-piece Stanton and Staveley lining, suggest that a line hinge may be more appropriate than the assumption of full continuity. Table 1 shows that good predictions in terms of the value of critical inner strain have resulted for boundary case 1 only, whereas in terms of critical defl ection, such a conclusion applies for boundary cases 3 and 5, but not for the other three cases. As for the previous two lining types, a stiff er response has resulted from the model. In addition to the presence of longitudinal joints, one must also point out that the defl ection values recorded for the Ce lining during the experiments were small, and hence
Results — Writing Task 129 the error induced in the readings might have further aff ected their accuracy. Observations of 2,4,6-trichlorophenol degradation by ozone 3. Results and discussion 3.1. Rate constants for the degradation of 2,4,6-TCP In previous studies degradation rate constants have been established by undertaking ozonation experiments (Graham et al., 2003) in the presence of a reference compound (Xiong and Graham, 1992a). Th e theoretical basis for this is as follows. Th e reaction of ozone with a solute M may be described by the following reaction scheme:
M + nO3 → Moxid (1) where n is the stoichiometric factor for the number of ozone molecules consumed per molecule of M degraded. The stoichio- metric factor for many organic substrates has been reported to vary in the range of 1–5 (Hoigne and Bader, 1983b), and values of 1 (Davis et al., 1995) and 2 (Javier Benitez et al., 2000a) have been proposed for 2,4,6-TCP. In practice it is usually assumed that the ozone reaction is first order with respect to ozone and solute M concentration, thus the rate law can be formulated as
−d[M]/dt = kM[O3] [M] (2) where kM is the rate constant for the degradation of solute M by O3. Previous work by the authors (Chu and Wong, 2003) has confi rmed that under conditions where the ozone concentration can be considered constant, the degradation of 2,4,6-TCP is fi rst order with respect to its concentration. In this study, in order to determine the degradation rate constant kM, ozonation has been conducted with a mixture of a solute M1 (2,4,6-TCP) and a reference compound M2 having a known rate constant (kM2 ). According to Eq. (2), it can be shown that
130 Science Research Writing
−d[M1]/dt = kM1 [O3] [M1] (3)
−d[M2]/dt = kM2 [O3] [M2] (4) Dividing Eq. (3) by (4), gives
d[M1] = kM1 [M1] (5)
d[M2] kM2 [M2] Integration of Eq. (5) yields
Ln [M1]0 = kM1 Ln [M2]0.
[M1]1 kM2
[M2]t
(6) Th us, a graph of Ln{[M1]0/[M1]} versus Ln{[M2]0/[M2]} yields a line whose gradient gives (kM1/kM2). Since the rate constant (kM2) of M2 is known, the value of kM1 can be determined. In these tests, the reference compound that was chosen was the herbicide atrazine (2-chloro-4-ethylamino-6-isopropylamino- 1,3,5-triazine) since rate constants for this had been determined previously under the same conditions (Xiong and Graham, 1992a). Figure 1 shows the results of the ozonation tests in terms of the comparative degradation of 2,4,6-TCP and atrazine. Th e calculated values for the rate constants for 2,4,6-TCP are shown in Table 1. 3.2. Reaction mechanism and dechlorination of 2,4,6-TCP Th e rate constants shown in Table 1 indicate that the reactivity of 2,4,6-TCP is much greater at neutral pH than at low pH; this can also be seen in Fig. 2. Th is is partly explained by the much lower reactivity of undissociated 2,4,6-TCP with molecular ozone than in its substantially dissociated state at pH 7.5, and partly by the eff ect of hydroxyl radical-reactions at the higher pH. Th e latter eff ect is predominant at high pH and a previous study has shown a linear increase in pseudo fi rst-order reaction rates with pH in the range of 7 < pH < 11 (Chu and Wong, 2003). Th e results shown in Fig. 2 indicate that in the early stages of the reaction there is a large overall O3:TCP reaction stoichiometry, thus, at a reaction time of