Nucleophilicity is a kinetic property. A higher nucleophilicity indicates that the nucleophile will easily donate its electrons to the electrophile and that the reaction will occur at the faster rate. The reaction rate also depends on the nature of the electrophile and solvent. Rank the following reactions from fastest to slowest based on the nucleophilicity of the nucleophile.

a. CH3NH- + CH3--Br → CH3NHCH3 + Br-
b. (CH3)2N- + CH3--Br → (CH3)2NCH3 + Br-
c. H2N- + CH3--Br → CH3NH2 +Br-

The rate constant (K) is related to activation energy (Ea), frequency factor (A) and temperature (T) in Kelvin by the equation

R = molar gas constant

K = A(e^(-Ea/RT))

Taking natural log of both sides

In K = In A - (Ea/RT)

In K = (-Ea/R)(1/T) + In A

Comparing this to the equation of a straight line; y = mx + c

y = In K, slope, m = (-Ea/R), x = (1/T) and intercept, c = In A

a) From the question, m = (-Ea/R) = -1.10 × (10^4) K

(-Ea/R) = -1.10 × (10^4) = -11000

R = 8.314 J/K.mol

Ea = -11000 × 8.314 = 91454 J/mol = 91.454 KJ/mol

b) c = In A = 33.5

A = e^33.5 = (3.54 × (10^14))/s

c) K = A(e^(-Ea/RT))

A = (3.54 × (10^14))/s, Ea = 91454 J/mol, T = 25°C = 298.15 K, R = 8.314 J/K.mol

K = (3.54 × (10^14))(e^(-91454/(8.314×298.15))) = 0.0336/s

QED!