In: Chemistry
At 326°C,1,3-butadiene dimerizes according to this equation: 2C4H6---->C8H12
In a given experiment, the initial pressure of 1,3-butadiene was 632.0 torr. Using the data table below, calculate the order of the reaction and the rate constant.
Time, min | Total Pressure,torr |
0.00 | 632.0 |
3.25 | 618.5 |
12.18 | 584.2 |
24.55 | 546.8 |
42.50 | 509.3 |
68.05 | 474.6 |
First we should write out the balanced reaction for this process
2C4 H 6 ? C8 H12
Initial n0 0
Time t n0 ? 2 x
x We are again assuming that 2x moles are being consumed in each step
From this, we can determine the number of moles at any given time, t.
n0 ? 2 x + x = n0 ? x
n0 ? x at time t
Using the Ideal Gas Law, we can derive expressions for the number of moles in both instances.
PV = nRT
P0 = n0 RT / V
P0 ? Pt = n0 RT / V - ( n ? x ) RT /V
P0 ? Pt = x RT /V
P0 ? Pt = xRT/ V
The partial pressure of butadiene at a time t, can therefore be expressed as
, PC4 H6 = 2 Pt ? P0 = ( n0 ? 2 x ) RT / V
e.g. at time 3.25min,
P t =618.5
Torr PC4 H6 (3.25) = 2 × 618.5 ? 632 = 605
t/min |
3.25 |
12.18 |
24.55 |
42.50 |
68.05 |
= 2 Pt ? Po |
605.0 |
536.4 |
461.6 |
386.6 |
317 |
Ln(PC H/P) |
-0.0437 - |
-0.1640 |
-0.3142 |
--0.4915 |
-0.6894 |
order to determine whether the reaction proceeds according to 1st or 2nd order kinetics, one should first plot CH vs.P t . This plot yields curved line
This means that the reaction does NOT proceed according to 1st order kinetics and therefore, we must now try to plot the inverse of the pressure versus time