The ame speed for a combustible hydrocarbone air mixture is known to be 30 cm/s.

Question

The ame speed for a combustible hydrocarbone air mixture is known to be 30 cm/s. The activation energy of such hydrocarbon reactions is generally assumed to be 160 kJ/mol. The true adiabatic ame temperature for this mixture is known to be 1600 K. An inert diluent is added to the mixture to lower the ame temperature to 1450 K. Since the reaction is of second order, the addition of the inert can be considered to have no other effect on any property of the system. Estimate the ame speed after the diluent is added

The answer is around 15 cm/s.

Explanation / Answer

from Arhenius Equation at two different temperatures (T1)= 1600K and T2= 1450K with rate constants K2= 30cm/s and K1=

ln(K2/K1)= (Ea/R)*(1/T1-1/T2)

Ea= 160 Kj/mol =160*1000 j/mol and R= 8.314 j/mol.k

ln(30/K1)= (160*1000/8.314)*(1/1450-1/1600)=1.244

30/K1= 3.47

K1= 30/3.47=8.645 cm/s

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