Question

Sam is a known snorer and of course cold blooded. What is interesting is that when he visits the in laws in Minnesota his snoring rate decreases. Sam recorded himself at night, recording the rate constant many nights, along with the temperature. He plotted one thing related to the rate constant versus another related to the temperature (you need to figure out exactly what) to give a slope of -220 K, and an intercept of 1.22, but then he took off for Hawaii without any more information. What is the activation energy and preexponential factor for Sam to snore? (units will be snores/second)

Answer 1

From Ahrrenius equation;

K1 = A*exp(-Ea/(RT1))

K2 = A*exp(-Ea/(RT2))

Note that A and Ea are the same, they do not depend on Temperature ( in the range fo temperature given)

Then

Divide 2 and 1

K2/K1 = A/A*exp(-Ea/(RT2)) / exp(-Ea/(RT1))

Linearize:

ln(K2/K1) = -Ea/R*(1/T2-1/T1)

get rid of negative sign

ln(K2/K1) = Ea/R*(1/T1-1/T2)

for a generic value:

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

where:

x-axis = 1/T ; inverse value of absolute temperature

y-axis = ln(K) , natural log of the rate constant

slope = -E/R or Acitvation Energy divided by Ideal Gas Constant

y-intercept = ln(A) ; natural log of the Frequency Factor

then

slope = -220

-220 = -E/R

E = 8.314*220 = 1829.08J/mol

b)

y-intercept = 1.22

ln(A) = 1.22

A = exp(1.22) = 3.387