Page 152 - [B._MURPHY,_C._MURPHY,_B._HATHAWAY]_A_working_meth

136 Chapter 9
Then: m = Ay/Ax = b2 - y1)/(x2 - xl), and do not forget
that the slope has units too.
9. The intercept of the graph, c, is then determined by examining
where the graph cuts the y-axis at x = 0. The units of c are
obviously the y-axis units. If, however, you find from the scale
of your graph that x = 0 is not included, c can still be
determined, without extrapolating (extending) the graph. To do
this, choose another independent point (x,, y,) on the line in the
centre of the graph, and use the formula:
y = mx + c + y, = rnx, + c + c = yc - rnx,, since m has
already been determined in step 8.
10. From the values of rn and c, determine the unknown para-
meter(@, e.g. Eact, A, etc.
11. Answer any riders to the question.

WORKED EXAMPLES

Example No. I: For the reaction A --$ Products, the following data
were obtained at 350 "C. Show graphically that this is a first-order
reaction and determine k, the specific rate constant for the reaction:
t/min 0 10 20 30 40
[Al/mM 2.51 2.05 1.53 1.10 0.86

Solution:

1. Read the question carefully-a graph needs to be drawn!
2. Two sets of data are given: time and concentration.
3. If first-order kinetics + ln[A] = - kt + ln[Ao]
y=mx+c
m = -kand c = In [Ao]
4. Need to obtain ln[A] values:
y-axis x-axis
"/mM In [A1 In [A1 t/min
2.51 0.9202828 0.920 0
2.05 0.7178398 0.718 10
1.53 0.4252677 0.425 20
1.10 0.0953 102 0.095 30
0.86 - 0.1508229 -0.151 40
5. Maximum value of x = 40; minimum value of x = 0.
+ A suitable x-axis scale is 0 to 50.