Question

On page 512 of your textbook, it states that “…a 10 o C increase in temperature increases the rate of a typical reaction by two or three times.” Is this the case for the decolorization of CV + ? Show your work using 2 of the average temperatures (from the data table) that differ by about 10 o C. The temps I have are 18.1'C and 28.1'C

Answer 1

Solution:

Arrhenius equation for the temperature dependence of rate constant is given by

K = A exp(_E_a/RT) where A is the Arrhenius parameter (also called pre-exponential factor), E_a is the activation energy, R is the universal gas constant, T is the temperature in abosolute scale and k is the rate constant.

Let k1 and k2 be the rate constants for the reaction at 18.1 °C (= 18.1 + 273 = 291.1 K)(T1) and at 28.1°C (= 28.1 + 273 = 301.1)(T2). Using Arrhenius equation we can write

K1= A e(-E_a/RT1)    ----------------- (1)

K2 = A e(-E_a/RT2)--------------------(2)

Dividing (2) by (1)

K2/k1 = exp(-E_a/RT2)/ A e(-E_a/RT1)   =    exp(-Ea/RT1-Ea/RT2)

K2/k1   =    exp-Ea/R(1/T2-1/T1)] = exp-Ea/R(T1 – T2/T1T2)--------------(3)

Taking E_a = 50 kJ/mol = 50,000 J/mol as the characteristic activation energy and R = 8.314 Jmol^-1K^-1

we get from equation (3)

K2/k1 =   exp (-50000/8.314)(291.1 – 301.1)/291.1 x 301.1 =   exp (-6013.95)(-10/87650.21)

             = exp(6013.95)(1.141 x 10^-4) = exp(0.686)   = 1.986 which is almost equal to 2

Thus a 10 °C rise in temperature increases the rate of a reaction increases by two times .

Note: Activation energy which is required for calculation is not provided in the question . Exp(X)/Exp (Y) = Exp (X-Y)