3. The gas phase reaction OH(g) + Cll/g) H,O(g) + CH(g) is second order overall

Question

3. The gas phase reaction OH(g) + Cll/g) H,O(g) + CH(g) is second order overall and first order in both reactants. The initial rate of appearance (measured at constant volume and temperature) of HO as a function of temperature is given in the table below. The initial concentration of OH and CH, is 0.500 mol m (a) Calculate the Arrhenius parameters for the rate constant, (b) Calculate the initial rate and concentration of OH and H,O after 1 ms at 250 K for the same initial pressure. T/K R/mol ms 284 509 838 1290 240 260 280 300

Explanation / Answer

the rate of appearance (R) of the reaction is given by

R= K[OH]2, since [OH]= [CH4]

R= Ko*e(-Ea/RT)* [OH]2, E = activation energy , R = gas constant = 8.314 J/mole.K, T is temperature in K.

initial [OH] = [CH4] =0.5 mol/m3

R/[OH]2= Ko*e(-Ea/RT)     (1)

R' = Ko*e(-Ea/RT), R' = R/[OH]2

so first calculate the LHS of Eq.1, by dividing with [OH]2 term.

ln R' = lnKo -Ea/RT

so a plot of lnR;' vs 1/T gives straight line whose slope is -Ea/R and intercept is lnKo.

so a plot of lnR' vs 1/T is shown below along with data points

from the plot, slope is -Ea/R= 1816, Ea= 1816*8.314 j/mole=15098.2 J/mole= 15.098 Kj/mole

lnKo = 14.60, Ko = 2191288

so the rate of formation is R' = 2191288*e-(15098.2/RT) ,

R == 2191288*e-(15098.2/RT) [OH]2

K= 2192188 e(-15098/RT)

at 250 K, K= rate constant = 2191288 *e(-15098/250*8.314) =1534.7

Rate of formation of H2O= rate of decomposition of OH- = 1534.7 [OH]2

rate of disapperance of [OH]

-d[OH]/dt= 1534.7*[OH]2

when the equation is iintegrated noting that at t= 0 [OH]= 0.5 moles/m3 and at t= 1*10-3 sec, [OH] =[OH]

1/[OH] = 1/0.5 +1534.7*1*10-3

[OH]= 0.283 moles/m3

at t=0 [H2O]= 0 and [H2O] = 0.5-0.283= 0.217 mole/m3

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