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

Determine the activation energy for the reaction.

Determine the frequency factor for the reaction.

Determine the rate constant at 10 ∘C.

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

Arhenius Equation can be written as

K= Koe^(-Ea/RT)

ko is frequency factor, Ea =activation energy and R= gas constant

lnK= lnK0 -Ea/RT

So a plot of lnK Vs 1/T gives a straight line having slope of -Ea/R and intercept K0, the frequeny factor

The slope is -Ea/R= -10770

and Ea= 10770*8.314 Joules/mole.K=89542 Joules/mole.K

lnKo= 26.78 ( intercept)

K0= Frequecny factor = e^(26.78)= 4.3*10¹¹

at 10 deg.c= 10+273.15 K

T= 283.15K and 1/T= 1/283.15=0.003532

from the equation

lnK(10 deg.c)= -10770*1/283.15+26.78=-11.26

K =1.29*10^-5

at 90 deg.c= 90+273.15 K= 363.15K

lnK(363.15)= -10770/363.15+ 26.78

K= 0.056294 /M.Sec The rate constant at 90 deg.c

Rate for second order reacton R= K*[C2H5Br] [OH-] =0.056294*0.155*0.260=0.002269 M/Sec