Question

The following data show the rate constant of a reaction measured at several different temperatures.

1.Use an Arrhenius plot to determine the activation barrier for the reaction.

2.Use an Arrhenius plot to determine frequency factor for the reaction.

Temperature (K)	Rate Constant (1/s)
300	1.01×10−2
310	3.18×10−2
320	9.30×10−2
330	0.255
340	0.658

Answer 1

Arrhenius equation

K=A exp(-Ea/RT)

Where,A=pre-exponential factor or frequency factor

Ea=activation energy

RT=average kinetic energy,R=gas constant,T=temperature

K=rate constant

Or,ln k=lnA-Ea/RT……………………….(1)

Plot graph between ln K (along y-axis)   vs 1/T (along x-axis)

The above equation (1) can be compared to equation of straight line y=mx+c

Y=lnK

m=slope=-Ea/RT

intercept=c=lnA

hence the value of activation energy Ea and A can be calculated from slope and intercept respectively

T(k)	1/T	K(s-1) (rounded off)	lnK
300	0.0033	0.0101	-4.6
310	0.0032	0.0318	-3.4
320	0.0031	0.0930	-2.4
330	0.0030	0.255	-1.4
340	0.0029	0.658	-0.4

Slope=-8686.36 K-1=-Ea/RT

Ea=8686.36*RT=8686.36*8.314 J/K .mol* 298K=21397212.73 J/mol=21397.212 KJ/mol

Intercept=0.5=lnA

A=exp 0.5=1.65