Physical Chemistry HELP?!

A particular first order reaction has a rate coefficient (k) of 1.35 x 10^2 (s^-1) at 25oC. What is the value of k (s^-1) at 75oC if the activation energy (Ea) is 85.6 kJ mol^-1?

Arrhenius equation..
k = A x exp (-Ea/RT)

where
k = rate constant
A = pre-exponential factor
Ea = energy of activation
R = gas constant
T = temperature in K

so..
k1 = A exp(-Ea / RT1)
k2 = A exp(-Ea / RT2)

rearranging.
k1 / exp(-Ea / RT1) = A
k1 / exp(-Ea / RT2) = A

since the both = A, they = each other
k1 / exp(-Ea / RT1) = k2 / exp(-Ea / RT2)

rearranging..
k1 / k2 = exp(-Ea / RT1) / exp(-Ea / RT2)

since a^b / a^c = a^(b-c)
k1 / k2 = exp (-Ea / RT1 - -Ea / RT2)
k1 / k2 = exp [ (Ea/R) x (1/T2 - 1/T1) ]..... .. this look familiar?

rearranging...
k1 = k2 x exp [ (Ea/R) x (1/T2 - 1/T1) ]

solving.. (letting T2, k2 = 25°C, 1.25x10^2 /s and T1 = 75°C)
k1 = (1.35x10^2 / s) x exp [ (85600 J/mol) / (8.314 J/molK) x (1 / (25+273.15) - 1 / (75+273.15) ) ]

k1 = ___ / s

*********
can you finish?

welcome

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

(k2/1.35 x 10^2 s-1) = e^((-85.6 kJ mol-1 / 8.314 J K−1 mol−1 )(1/348K - 1/298K))
k2 = 1.35 x 10^2 s-1 x 143.18 = 19329.3 s-1