Question

When ethyl chloride, CH3CH2Cl, is dissolved in 1.0 M NaOH, it is converted into ehanol, CH3CH2OH, by the reaction CH3CH2Cl + OH– -> CH3CH2OH + Cl– At 25°C the reaction is first order in CH3CH2Cl, and the rate constant is 1.0 x 10–3 s–1. If the activation parameters are A = 3.4 X 1014 s–1 and Ea = 100.0 kJ/mol, what will the rate constant be at 40.°C?

Answer 1

Arhenius equation can be written as K= Ko e-Ea/RT

where K= rate constant , Ea= Activation energy, R= 8.314 j/mol.K T = temperature in K and Ko= Frequency factro

taking ln the equartion can be written as

lnK= lnK0-Ea/RT

at two different temperatures T1 and T2

the equation can be written as

ln *(K2/K1)= (Ea/R)*(1/T1-1/T2)   (1)

T1= 25 deg.c= 25+273.15= 298.15 K, T2= 40 deg.c= 40+273.15= 313.15K

K1= 1*10^-3 /sec and K2= ?   Ea= 100 Kj/mol= 100*1000 j/mol

Eq.1 becomes with these values

ln(K2/1*10^-3)= (100*1000/8.314)*(1/298.15-1/313.15)=1.932387

K2/1*10^-3= 6.91

K2= 6.91*1*10^-3 /sec