Chemical Kinetics Part 1

According to Arrhenius theory,
k=Ae−Ea∕RT
(k is the rate constant, A is Arrhenius factor, Ea= Activation energy, T is absolute temperature and R is gas constant.)
ln‌k=ln‌A−

Ea

RT

At temperature T1,
ln‌k1=ln‌A−

Ea

RT1

...(i)
At temperature T2,
ln‌k2=ln‌A−

Ea

RT2

...(ii)
Subtracting Eqs. (ii) from (i),
ln‌k1−ln‌k2=

Ea

R

(

1

T2

−

1

T1

)
ln‌

k1

k2

=

Ea

R

(

1

T2

−

1

T1

)
2.303‌log‌

k1

k2

=

Ea

R

(

1

T2

−

1

T1

)
log‌

k1

k2

=

Ea

2.303R

(

1

T2

−

1

T1

)
At, T1=700K,k1=6.36×10−3s−1,Ea =209kJmol−1,
R=8.314JK−1mol−1
At, T2=600K,k2=x×10−6s−1
log‌

6.36×10−3

x×10−6

=

209

2.303×8.314

(

1

600

−

1

700

)
=

209

2.303×8.314

(

100

420000

)
x = 16.