Page 140 - [B._MURPHY,_C._MURPHY,_B._HATHAWAY]_A_working_meth

124 Chapter 8
5. Overall order of the reaction = x + y + z = 1 + 3 - 1 = 3".
6. Determination of k: Rate = k[A]'[B]3[C]-1.
There are four initial rates given in the question. k must be
evaluated for each of these rates and then an average value
should be obtained:

k = (4.8)/(0.1)'(0.2)3(0.3)-1 = 1.8 x lo3
k = (9.6)/(0.2)1(0.2)3(0.3)-' = 1.8 x lo3
k = (0.6)/(0.1)'(0.1)3(0.3)-1 = 1.8 x lo3
k = (19.2)/(0.2)'(0.2)3(0.15)-' = 1.8 x lo3
Average value of k = 1.8 x lo3

7. Units of k: k = rate/[concentrationI3 + k has units of Ms-'/M3
-
- M-2 s-l
Answer: The reaction is first-order w.r.t. A, third-order w.r.t. B and has
order -1 w.r.t. C. The overall order of the reaction is third-order.
Average value of k, the specific rate constant = 1.8 x 1d s-l

Note: Sometimes, the partial orders can be obtained directly by
inspection. For example, in the above problem, if the concentra-
tions of B and C (0.2 and 0.3 M) are kept constant, doubling the
concentration of A (0.1 to 0.2 M) doubles the rate (4.8 to 9.6
M s-I). Therefore the reaction must be first-order with respect to
A. However, caution must be applied here, as this skill only comes
with experience. In the next example, such an initial deduction is
much more difficult, and hence the working method might be a
better place to begin, to evaluate the partial orders.

Example No. 2: Determine the approximate overall order for the
reaction: A + B + C + Products, from the following experimental
data, obtained by the method of initial rates:

[A]/M [B]/M [C]/M Initial Rate/M s-l
Rate 1 0.856 0.198 0.699 2.94 x 10-4
Rate2 0.593 0.198 0.699 9.76 x 10-5
Rate3 0.391 0.699 0.699 6.91 x 10-5
Rate 4 0.496 0.325 0.51 1 1.37 x 10-4