Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

APPENDIX 2 415TABLE 6 (continued)(C) DISTRIBUTION OF INDIVIDUAL VALUES ABOUT GROUP MEANSThe object is to calculateu=l i=land thence ms,.1 - 6.7 44.89 0.189 8.482 -22.0 484.00 0.444 214.903 11.1 123.21 1 .OOo 123.211 5.7 32.49 0.077 2.502 - 4.8 23.04 0.093 2.141 0 0 0.694 0u=.3 i=r,.*. s.s.~ = X C ~ (k~J(k~i-&~)~ = 351.23u=l i=lr-u = 6-3 = 3:. ms, = 117.1(d) CALCULATION OF FF=-=- msl 14.53ms, 117.1sum over set 351.23Clearly F c 1 and hence the set is homogeneous. The maximum value that F could take in 95 %of cases if the set were homogeneous is 9.55 (2 degrees of freedom in numerator, 3 in denominator).(e) BEST VALUE OF THE RATE COEFFICIENT AND AN ESTIMATE OF ITS STANDARD ERRORSince the set is homogeneous, the best value of the rate coefficient is the weighted mean, A,i.e. 7.139 x lo-' sec-'.The best estimate of s(J) is found from the larger of the two values msl or ms,, thusu=l i=l.*. s(6) = 6.9 x lod sec-I(f) CALCULATION OF THE 90 % CONFIDENCE LIMITS FOR THE urn COEFFICIENTSince the value ms4 used above in calculating s(K) was based on 3 degrees of freedom. we requirethe value oft appropriate to this number. From tables,t = 2.35The 90 % confidence limits for the ate coeflicient are, therefore,(7.139h2.35 x0.069) x lo-' ~e+-~^= (7.139h0.16)~ lo-* sec-lIn other words, we expect that the true value of the rate coefficient will lie between (6.98 and 7.30)X sec-I with 90 % confidence.