Question

The kinetics of the following second-order reaction were studied as a function of temperature:
C2H5Br(aq)+OH−(aq)→C2H5OH(l)+Br−(aq)

Temperature (∘C)	k (L/mol⋅s)
25	8.81×10−5
35	0.000285
45	0.000854
55	0.00239
65	0.00633

If a reaction mixture is 0.155 M in C2H5Br, and 0.260 M in OH−, what is the initial rate of the reaction at 90 ∘C?

Answer 1

For the given reaction,

Energy of activation Ea

using arrhenius equation,

ln(k2/k1) = Ea/R[1/T1 - 1/T2]

T1 = 25 + 273 = 298 K

T2 = 35 + 273 = 308 K

k1 = 0.000285 L/mol.s

k2 = 0.000854 L/mol.s

R = gas constant

we get,

ln(0.000854/0.000285) = Ea/8.314[1/298 - 1/308]

Ea = 83744.941 J/mol

let us find the rate constant at 90 oC.

using arrhenius equation,

ln(k2/k1) = Ea/R[1/T1 - 1/T2]

with,

T2 = 90 + 273 = 363 K

k2 = rate constant at 90 oC

we get,

ln(k2/0.00633) = 83744.941/8.314[1/338 - 1/363]

k2 = 0.0493 L/mol.s

This is a second order reaction so,

initial rate at 90 oC = k2[C2H5Br][OH-]

                               = 0.0493(0.155)(0.260)

                               = 1.987 x 10^-3 L/mol.s