Question

Part A A certain first-order reaction has a rate constant of 2.40×10−2 s−1 at 21 ∘C. What is the value of k at 61 ∘C if Ea = 90.0 kJ/mol ? Express your answer using two significant figures. k = s−1 SubmitMy AnswersGive Up

Part B A certain first-order reaction has a rate constant of 2.40×10−2 s−1 at 21 ∘C. What is the value of k at 61 ∘C if Ea = 104 kJ/mol ? Express your answer using two significant figures. k = s−1 SubmitMy AnswersGive Up

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=90J=90*10^3J
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' ) ]

Given K=240*10^-2 s^-1

K'= ?

T= 21oC=21+273=294 K

T'= 61oc= 61+273= 334 K

Plug the values we get K'= 1.97 s^-1

Similarly when Ea= 104 kJ/mol K'= 4.0*10^-2 s^-1