Arrhenius Equation?

Question

A(g) + B(g) ---> C(g)

The rate law for the above reaction is:

-d[A]/dt = k[A][B]

The rate constant is 2.90×10-4 L mol-1 s-1 at 339°C and 4.24×10-2 L mol-1 s-1 at 533°C.

Use the Arrhenius equation

k = Ae-Ea/RT

to:

Calculate Ea for this reaction.
1.05×102 kJ/mol

Calculate the rate constant k at 413°C for this reaction.

i know there is one formula like ln(k2/k1)=Ea/R(1/T1-1/T2)

can anybody helps please?i have no idea how to do this..

Answer 1

You already have the equation you just need to plug-in the values.

First of all how to get the equation yourself
k1= Ae^-Ea/RT1
k2= Ae^-Ea/RT2

divide the two =>
k1/k2= e^-(Ea/RT1-EaRT2) = e^-(Ea/R)(1/T1-1/T2) =>

ln(k1/k2)= -(Ea/R)* (1/T1-1/T2) =>
ln(k2/k1) =(Ea/R) *(1/T1-1/T2)

R=8.314 J*K^-1*mole^-1
k1=2.9*10^-4
k2= 4.24*10^-2
T1= 339+273 = 612
T2= 533 +273b= 806 so substitute and find Ea in J/mol

Once you have that, you use the same equation to find k2' for T2'= 273+413= 686.