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The rate constant for a reaction was determined to be 4.25 * 10 ^ -3 L/mol*s...

The rate constant for a reaction was determined to be 4.25 * 10 ^ -3 L/mol*s at 22.5 C. The rate constant was then measured at 48.0 C and found to be 1.95 * 10 ^ -2 L/mol*s. Calculate the value of the activation energy. Is the reaction first of second order?

PLEASE EXPLAIN THIS AS MUCH AS POSSIBLE INCLUDING EVERY LITTLE STEP IN THE ANSWER. Thank you so much!

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Answer #1

According to Arrhenius Equation , K = A e -Ea / RT
Where
K = rate constant
T = temperature
R = gas constant = 8.314 J/mol-K
Ea = activation energy
A = Frequency factor (constant)
Rate constant, K = A e - Ea / RT
log K = log A - ( Ea / 2.303RT ) ---(1)
If we take rate constants at two different temperatures, then
log K = log A - ( Ea / 2.303RT ) --- (2)
& log K' = log A - (Ea / 2.303RT’) ---- (3)
Eq (3 ) - Eq ( 2 ) gives
log ( K' / K ) = ( Ea / 2.303 R ) x [ ( 1/ T ) - ( 1 / T' ) ]
Ea = [(2.303R x T x T’) / (T’ - T)] x log (K’ / K)  

T= 22.5oC=22.5+273= 295.5 K

T'= 48oC= 48+273=321 K

K= 4.25*10^-3 L/mol-s

K'= 1.95*10^-2 L/ mol*s

Plug the values we get Ea= 47.125*10^3 J= 47.125 kJ

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