A certain first-order reaction has an activation energy of 53 kJ mol -1 . It is

Question

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

Explanation / Answer

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

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