The uncoiling of the DNA double helix is a first-order process with an activatio
ID: 932087 • Letter: T
Question
The uncoiling of the DNA double helix is a first-order process with an activation energy of about 420 kJ/mol. Because of the rather large activation energy, the reaction rate is extremely sensitive to temperature. At 50°C, the uncoiling proceeds fairly quickly, with a half-life of 2.0 minutes. What is the half-life at normal body temperature (37°C)? HINT: Recall that in class we showed that for a first-order reaction the half-life is related to the rate constant by the following equation. t1/2 = ln 2 k
Explanation / Answer
at 50 oC t1/2 = 2.0 min
rate constant k would be for a first order reaction,
k = 0.693/t1/2 = 0.693/2 = 0.3465 min-1
Using Arrhenius relation,
ln(k2/k1) = Ea/R[1/T1 - 1/T2]
with,
k1 = ?
k2 = 0.3465 min-1
T1 = 37 oC = 37 + 273 = 310 K
T2 = 50 oC = 50 + 273 = 323 K
Ea = 420 kJ/mol
R = 8.314 J/K.mol
we get,
ln(0.3465/k1) = 420000/8.314 [1/310 - 1/323]
k2 = 4.912 x 10^-4 min-1
Thus, half life would be = 0.693/k = 0.693/4.912 x 10^-4 = 1410.722 min
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