Question

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

Answer 1

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