Cinética Química e Logaritmos

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578 17 CHEMICAL KINETICS
−2.2 −2.1 −2.0 −1.9 −1.8
2.0
2.5
3.0
case (ii)
case (i)
log([complex]/moldm−3)
lo
g(
υ 0
/m
ol
dm
−3
s−
1 )
Figure 17.1
Similarly, for case (ii) the intercept is log υ0/moldm−3 s−1 = 4.868 which cor-
responds to υ0 = 7.37... × 104 moldm−3 s−1 when [complex] = 1 mol dm−3.
Hence
kr,eff ,ii =
υ0
[complex]
= 7.37... × 10
4 moldm−3 s−1
1 mol dm−3 = 7.37... × 104 s−1
Because kr,eff = kr[Y]b , taking the logarithm gives
log kr,eff = log kr + log[Y]b = log kr + b log[Y]
where the properties of logarithms log(xy) = log x + log y and log xa = a log x
are used.
�is expression implies that a graph of log kr,eff against log[Y]will be a straight
line of slope b. However, because there are only two data points, one for [Y] =
2.7mmol dm−3 and one for [Y] = 6.1mmol dm−3, a graph is not necessary and
an alternative approach is used.�e two data points give the equations
log kr,eff ,i = log kr + b log[Y]i and log kr,eff ,ii = log kr + b log[Y]ii
Subtracting the second equation from the �rst gives
log kr,eff ,i − log kr,eff ,ii = b log [Y]i − b log[Y]ii
Hence, using log x − log y = log(x/y),
log( kr,eff ,i
kr,eff ,ii
) = b log( [Y]i
[Y]ii
)
Rearranging for b gives
b = log (kr,eff ,i/kr,eff ,ii)
log ([Y]i/[Y]ii)
=
log [(1.66... × 104 s−1)/(7.37... × 104 s−1)]
log [(2.7 mmol dm−3)/(6.1 mmol dm−3)]
= 1.83 . . .