Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

~~414 TREATMENT OF EXPERIMENTAL DATATABLE 6The calculations set out in this table show that the six rate coefficients listed in Table 3 determinedat three different initial concentrations of isoprene constitute an homogeneous set(a) CALCULATION OF GROUP AND SET MEANSOriginal Number Number1 Wk,, l@s(kvd) 10-12w(kvi) lO-*w(k,,)k,,number of ofrun 3 7 Seca secof run group within0 group 10-12isec2s2(k,,)1 1 7.097 2.3 0.189 1.3412 1 2 6.944 1.5 0.444 3.0833 3 7.275 1.0 1.000 7.275sums over group 1.633 11.699104 Cw(k,,)k,,lo4& =~-11.699sec-l 1.633= 7.1644521 7.155 3.6 0.077 0.55092 7.050 3.3 0.093 0.6557sums over group 0.1701.2066 10%~ = 1.2066__-sec-l 0.170= 7.0986 31 7.091 1.2 0.694 4.921 1 mean k forsums over set 2.497 17.827110% =--17.8271sec-l 2.497= 7.139(b) DISTRIBUTION OF GROUP MEANS ABOUT SET MEANAs shown above, the whole set comprises three groups; in group 1, there are 3 experiments, ingroup 2, 2 experiments and group 3, 1 experiment; therefore, rl = 3, ra = 2 and ra = 1. Theobject is to calculateu=3 1=r,B C w(k,,)(K,-K)*and thence ms,Number ofgroup1)Y'110d(K,-A)seC-1i=l1 2.5 6.25 1.633 10.2062 -4.1 16.81 0.170 2.8583 -4.8 23.04 0.694 15.990u=3 i=ry:. s.s.1 = C C w(kv,)(K,-R)a = 29.054u=l 1=1U-1 = 3-1 = 2:. m, = 14.53sum over set 29.054