In: Chemistry
A certain first-order reaction has an activation energy of 53 kJ mol-1. It is run four times, once at 298 K, again at 308 K, a third time at 398 K, and finally at 408 K. Assume that k1 = rate constant at 298 K, k2 = rate constant at 308 K, k3 = rate constant 398 K, and k4 = the rate constant at 408 K. Assuming that all other factors are identical, identify the correct ratios between rate constants for this reaction.
a) k1:k2 is 1 to 2
b) k1:k2 is 1 to 4
c) k1:k3 1 to 150
d) k2:k3 is 1 to 160
e) k3:k4 is 1 to 1.5
f) k3:k4 is 1 to 150
correct ratios
a) k1:k2 is 1 to 2
e) k3:k4 is 1 to 1.5
Arrhenius equation
ln(K2/k1) = Ea/R[1/T1 - 1/T2]
k1 = 1 , T1 = 298 k
k2 = x, T2 = 308 k
Ea = 53 kj/mol , R = 8.314*10^-3 j.k-1.mol-1
ln(x/1) = (53/(8.314*10^-3)((1/298)-(1/308))
k2/k1 =2/1
so that, k1:k2 = 1:2
ln(K3/k1) = Ea/R[1/T1 - 1/T3]
k1 = 1 , T1 = 298 k
k3 = x, T3 = 398 k
Ea = 53 kj/mol , R = 8.314*10^-3 j.k-1.mol-1
ln(x/1) = (53/(8.314*10^-3)((1/298)-(1/398))
k3/k1 = 216/1
so that, k3:k1 = 216:1
ln(K3/k1) = Ea/R[1/T1 - 1/T3]
k2 = 1 , T2 = 308 k
k3 = x, T3 = 398 k
Ea = 53 kj/mol , R = 8.314*10^-3 j.k-1.mol-1
ln(x/1) = (53/(8.314*10^-3)((1/308)-(1/398))
k3/k2 = 107.8 /1
ln(K4/k3) = Ea/R[1/T3 - 1/T4]
k3 = 1 , T3 = 398 k
k4 = x, T4 = 408 k
Ea = 53 kj/mol , R = 8.314*10^-3 j.k-1.mol-1
ln(x/1) = (53/(8.314*10^-3)((1/398)-(1/408))
k4/k3 = 1.5/1
so that, k3:k4 = 1 : 1.5