ah3pod state 3 The first-order rearrangement of CH3NC is measured to have a rate

Question

ah3pod state 3 The first-order rearrangement of CH3NC is measured to have a rate constant of 3 61 x 10-15 s-1 at 298 K and a rate constant of 8.66 x 10-7 s-1 at 425 K. Determine the activation energy for this reaction. A) 160. kJmol B) 240. kJ/mol C) 417 kJ/mol D) 127 kJ/mol E) 338 kJ/mol 4. The age of an ancient tree trunk is estimated using radiocarbon dating. If the trunk has a C-14 decay rate that is 34% of what it is in living plants, how old is the trunk? The half-life of C-14 is 5730 years. F3 F4 F5 F6 F7 FB #9 F10

Explanation / Answer

A) 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)  

Ea= [2.303x8.314x298x425/(425-298)]x log((8.66*10^-7)/(3.61*10^-15)(

=160*10^3 K

= 160 kJ

C)For a first order reaction rate constant , k = ( 2.303 /t )x log ( Mo / M)
Where
Mo = initial mass= 100%
M= Mass left after time t = 34%
t = time = ?

k= rate constant= 0.693/half life= 0.693/5370 yr=1.3*10^-4 yr^-1

Plug the values we get t= 8361yrs

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