On Monday, October 5, the department hosted a seminar from Dr. Bill Jones of the

Question

On Monday, October 5, the department hosted a seminar from Dr. Bill Jones of the University of Rochester. Dr. Jones' research students and collaborators have contributed multiple papers to the chemical literature over the last several years. (See, for example, y GT 4C5articles cited at the end of this exam.) His group found that, at a given temperature (assume 25 degree ), a given metal, M, preferentially bound to methylene sites in an alkane, rather than the terminal methyl sites. If the binding of M to -CH2- occurs at a rate 1.5 times the rate of M binding to -CH3, what is the difference in activation energy for those two elementary reactions? What temperature(s) would you run the reaction at to shift the relative binding rates from 1.5:1 to 10:1? c. to 1000:1?

Explanation / Answer

(1) M + A = MA1
(2) M + A = MA2

(a)
Elementary reactions, so
rate1 = k1*[M]*[A]
rate2 = k2*[M]*[A]

rate1/rate2 = k1/k2 = 1.5
Temperature, T=25+273=298K
Gas constant, R = 8.314 J/mol-K
Arrhenius equation, k = A*exp(-Ea/(R*T))
Same reactants so, A is constant.
k1/k2 = exp((Ea2-Ea1)/(R*T))
Ea2 - Ea1 = R*T*Ln(k1/k2)=8.314*298*Ln(1.5)=1005 J/mole

(b)
k1/k2=10
k1/k2 = exp((Ea2-Ea1)/(R*T))
T = (Ea2-Ea1)/{R*Ln(k1/k2)} = 1005/(8.314*Ln(10)) = 52.5 K

(c)
k1/k2=1000
T = (Ea2-Ea1)/{R*Ln(k1/k2)} = 1005/(8.314*Ln(1000)) = 17.5 K

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