Answer:
a) the activation barrier = 122.3 kJ/mol
b) The rate constant at 425 K = 0.1001 /s
Step-by-step explanation:
Step 1: Data given
Rate constant k1 = 1.15 * 10^−2 /s at 400K (= T1)
Rate constant k2 = 0.685 /s at 450K (=T2)
Step 2: Determine the activation barrier for the reaction.
To determine the activation energy we will use the two-point Arrhenius equation:
ln(k₂/k₁) = (Ea/R)((1/T1) - (1/T2))
⇒ with Ea = the activating energy
⇒ with R = the gas constant = 8.314 J/mol* K
⇒ with k1 = rate constant 1 = 1.15 *10^-2 /s
⇒ with T1 = Temperature 1 = 400 K
⇒ with k2 = rate constant 2 = 0.685/s
⇒ with T2 = temperature 2 = 450 K
= - (Ea/R)(T₁ - T₂)/T₁T₂
Ea = (R*ln (k2/k1)) / ((1/T1)- (1/T2))
Ea = (8.314* ln(0.685/0.0115)) / ((1/400) - (1/450))
Ea = 122327.6 = 122.3 kJ/mol
B) What is the value of the rate constant at 425 K
For rate constant at 425 K.
Substitute the value of activation energy as 122327.6 J/mol, initial temperature as 400 K, final temperature as 425 K, rate constant at 400 K
1/T1 - 1/ T3 = 1/400 - 1 /425 = 1.47*10^-4
⇒ with T1 = the initial temperature = 400 K
⇒ with k1 = the rate constant at 400 K = 1.15 * 10^-2 /s
⇒ with T3 = the nex temperature = 425 K
⇒ with k3 = the rate constant at 425 K
ln(k3/k1) = Ea/R * ((1/T1)- (1/ T3))
⇒ with k3 = the rate constant at 425 K
⇒ with T3 = 425 K
k3/k1 = e^(Ea/R * ((1/T1)- (1/ T3)))
k3 = k1* e^(Ea/R * ((1/T1)- (1/ T3)))
k3 = 0.0115 * e^(122327.6/8.314 * (1.4710^-4))
k3 = 0.0115* e^2.1643
k3 = 0.1001 /s