emistry 325/525 esday, December 05, 2017 Week 14 Lecture1 3) Using the data in t

Question

emistry 325/525 esday, December 05, 2017 Week 14 Lecture1 3) Using the data in the table, determine the order of the reaction and calculate the rate constant for the dimerization of butadiene in the gas phase at 326 °C. The rea given by 2C,H-CH2. Hint, derive a relationship that relates the pressure to the concentration of the reactant by constructing a table and using the extent of reaction, or x. Next, plot the data assuming the reaction is either first or second order and use ction is the plot to determine the order. time (min) total P (mm Hg) 0 6.1 12.2 17.3 29.2 42.5 60.9 90 119 176.7 632 607 584 567 535 509 483 453 433 405 yny A

Explanation / Answer

for the reaction, 2C4H6--------> C8H12,

PA= PAO- (a/deltan)*(Pi-Po)

where PAO= initial partial ppressure of C4H6, Pi= total pressure at time t and Po= initial total pressure

a= coefficient of the reactant C4H6 =1, PA= pressrue of A at any time

deltan= change in no of mole during the reaction = 1-2=-1

PA= PAO+ 2*(PI-Po)

hence thae data on ttotal pressure need to be converted to PA.

the data on pressure will be converted to atm, since 760 mm = 1 atm.

since CA= PA/RT, the data on pressure will be converted to concentration by noting that R= 0.0821 L.atm/mole K. and T= 326 deg.c =326+273= 599K. This calculations are also shown in the table below

the relation between order (n) rate constant and rate is

-dCA/dt= K[A]n, n=0 refers to zero order and n=1 refer to 1st oder and n= 2 refer to second order.

when n=0, the reaction is zeo order the integrate equation becomes CA= CAO- Kt, where CAO= initial concentration

so a plot of CA vs t has to be straight line for zero order.

for n=1 it is 1st order and lnCA= lnCAO-Kt is the integrated equation and hence a plot of lnCA vs t has to be straight line.

for n=2 , second order, 1/CA= 1/CAO+ Kt, so a plot of 1/CA vs t has to be straight line.

All the three plots are drawn and shown below.

from the plot of best fit is 1/CA Vs t and the reaction is seond order with rate constant from the slope =0.849/M.sec

PAO (mm Hg) Po (mm Hg) PA (mm Hg) PA(atm) R( L.atm/mole.K) T(K) CA=PA/RT Time(min) CA lnCA 1/CA 632 632 632 0.831579 0.0821 599 0.01691 0 0.01691 -4.07987 59.13798 632 632 582 0.765789 0.0821 599 0.015572 6.1 0.015572 -4.16229 64.21856 632 632 536 0.705263 0.0821 599 0.014341 12.2 0.014341 -4.24463 69.72986 632 632 502 0.660526 0.0821 599 0.013431 17.3 0.013431 -4.31016 74.4526 632 632 438 0.576316 0.0821 599 0.011719 29.2 0.011719 -4.44654 85.33152 632 632 386 0.507895 0.0821 599 0.010328 42.5 0.010328 -4.57293 96.82695 632 632 334 0.439474 0.0821 599 0.008936 60.9 0.008936 -4.71762 111.9018 632 632 274 0.360526 0.0821 599 0.007331 90 0.007331 -4.91563 136.4059 632 632 234 0.307895 0.0821 599 0.006261 119 0.006261 -5.07344 159.7231 632 632 178 0.234211 0.0821 599 0.004763 176.7 0.004763 -5.34698 209.9731

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