Given:
Ea(Activationenergy):49.4kJ/molecule
k1: the rate constant of the first reaction
k2 : rate constant of the second reaction.
T2: Temperature of the second reaction.
T1: Temperature of the first reaction.
k2/k1=4.55
Now by Arrhenius equation we get
log(k2/k1)=[Ea/(2.303xR)] x[(1/T1)-(1/T2)]
Where k1 is the rate constant of the first reaction.
k2 is the rate constant of the second equation.
T2 is the temperature of the second reaction measured in K
T1 is the temperature of the first reaction measured in K
Ea is the activation energy kJ/mol
R is the gas constant measured in J/mol.K
Now substituting the given values in the Arrhenius equation we get:
log(k2/k1)=[Ea/(2.303xR)] x[(1/T1)-(1/T2)]
log(4.55)=[Ea/(2.303xR)] x[(1/T1)-(1/T2)]
0.66=[49.4/(2.303x8.314x10^-3)]x[(1/355)-(1/T2)]
0.66= 2579.75x [(1/355)-(1/T2)]
0.000256= (T2-355)/355T2
0.0908T2-T2= -355
0.9092T2=355
T2=390.46K
