Hydrolysis of the high explosive hexahydro-1, 3, 5-trinitro-1, 3, 5-triazine (RD

Question

Hydrolysis of the high explosive hexahydro-1, 3, 5-trinitro-1, 3, 5-triazine (RDX) proceeds according to first-order kinetics. Experiments were conducted at five temperatures and the data for the first-order reaction rate constants are given versus temperature in the following table: Determine the Arrhenius: activation energy Ea (kJ/mol) A RDX waste stream is discharged into a stream resulting in a concentration of 50 mg/1. The temperature of the stream water immediately after the point of discharge is 10 degree C. If hydrolysis is the only transformation mechanism in the stream, determine the time it will take to reach a concentration of 10 mg/l. If the river velocity is 5 mi/hr determine the distance downstream that this concentration (10 mg/l) can be attained.

Explanation / Answer

for calculating the activation energy, a plot of 1/T ( Temperature in K) vs lnK needs to be drawn.

lnK= lnKo- Ea/RT

So the slope of the plot is -Ea/R, where Ea= activation energy

the plot along with the data points is shown below

Ea/R ( the slope from the plot) =7233

Ea= 7233*8.314 J/mole = 60135.16 J/mole= 60.135 Kj/mole

for 1st order kinetics

lnC= lnCO- Kt where C= Concentration at any time, t , CO= initial concentration, K= Rate constant

at 10 deg.c

ln10= ln(50)- 0.112*t, 2.302= 3.912-0.112t

t= 14.37 hr

3. Assuming the temperature is at 10deg.c, the distance at which the concentration will be 10mg/L for a river velocity of 5mi/hr= 5mi/hr*14.37hr= 71.85 hrs

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