A.) Determine Ea for the forward reaction; assume that the value is independent

Question

A.) Determine Ea for the forward reaction; assume that the value is independent of temperature

B.) Determine Ea for the reverse reaction; assume that the value is independent of temperature

C.) Determine the standard enthalpy ?H? change for the reaction (assumed independent of temperature)

D.) Calculate the equilibrium constant for duplex formation at 46.7?C.

The kinetics of double-strand formation for a DNA oligonucleotide containing a G T base pair was measured by temperature-jump kinetics. The reaction is 2CGT GAATTC GCG DUPLEX k-1 The following data were obtained: Temperature (OC) ki (10 M s 1) k-1 (s 1) 1.00 0.8 31.8 36.8 2.3 3.20 15.4 41.8 3.5 46.7 6.0 87.0

Explanation / Answer

(a): For forward reaction:

T1 = 31.8 DegC = 31.8 + 273 = 304.8 K

k1 = 0.8x105 M-1s-1

Applying Arrhenius equation

k1 = A x (exp)(-Ea / RT)  

=> 0.8x105 M-1s-1 =  A x (exp)(-Ea / Rx304.8K) -------- (1)

T2 = 36.8 DegC = 36.8 + 273 = 309.8 K

k2 = 2.3x105 M-1s-1

Applying Arrhenius equation

k2 = A x (exp)(-Ea / RT2)  

=> 2.3x105 M-1s-1 =  A x (exp)(-Ea / Rx309.8K) -------- (2)

Now we can find the value of Ea by dividing eqn(1) and eqn(2)

=> (0.8 / 2.3) = (exp)(Ea/309.8R) - (Ea/304.8R)

=> ln(0.8 / 2.3) = (Ea/R)x[1/309.8 - 1/304.8] = - (Ea / 8.314 JK-1mol-1) x [ 5 / 309.8x304.8]

=> Ea = 165814 J/mol = 170 kJ/mol (answer)

(b): Reverse reaction:

T1 = 31.8 DegC = 31.8 + 273 = 304.8 K

k1 = 1.00 s-1

Applying Arrhenius equation

k1 = A x (exp)(-Ea / RT1)  

=> 1.00 s-1 =  A x (exp)(-Ea / Rx304.8K) -------- (1)

T2 = 36.8 DegC = 36.8 + 273 = 309.8 K

k2 = 3.20 s-1

Applying Arrhenius equation

k2 = A x (exp)(-Ea / RT2)  

=> 3.20 s-1 =  A x (exp)(-Ea / Rx309.8K) -------- (2)

Now we can find the value of Ea for reverse reation by dividing eqn(1) and eqn(2)

=> (1.00 / 3.20) = (exp)(Ea/309.8R) - (Ea/304.8R)

=> ln(1.00/3.20) = (Ea/R)x[1/309.8 - 1/304.8] = - (Ea / 8.314 JK-1mol-1) x [ 5 / 309.8x304.8]

=> Ea = 182630 J/mol = 180 kJ/mol (answer)

(d): Given T = 46.7 DegC = 46.7 + 273.15 = 319.85 K

At T = 319.85 K, forward rate constant, k1 = A x (exp)(-Ea / Rx319.85K)

=>  k1 = A x (exp)(-165814 Jmol-1/ Rx319.85K)

reverse rate constant, k-1 =  A x (exp)(-Ea / Rx319.85K)

=> k-1 =  A x (exp)(-182630 Jmol-1 / Rx319.85K)

Equilibrium constant K = k1 / k-1 = (exp)^(182630 Jmol-1 / Rx319.85K - 165814 Jmol-1/ Rx319.85K)

=> K = (exp)^(16816 / 319.85x8.314) = 557.6 (answer)

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