Question

The rate of a certain reaction was studied at various temperatures. The table shows temperature (T) and rate constant (k) data collected during the experiments. Plot the data, and then answer the following questions.

What is value of the activation energy, E_a for this reaction

What is the value of the pre-exponential factor (sometimes called the frequency factor), A, for this reaction

 

Answer 1

Ahrrenius Plot 1 point

We must plot via ---> Ahrrenius Equation for 1 and several Points

According to Arrhenius, we can relate the rate constants as following:

K = A*exp(-Ea/(RT))

Where:

K = rate constant at Temperature “T”

A = Frequency Factor

E = Activation Energy in J/mol

R = ideal gas constant, 8.314 J/mol-K

T = absolute temperature

Ahrrenius Equation 2 Points

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

From the slope

Slope =-16119

slope = -Ea/R

solve for Ea

Ea = 16119*R = 16119*8.314 = 134013.366 J/molK

Ea = 134.01 kJ/mol

B)

for a

y-intercept = ln(A)

y-intercept = 32.107

ln(A) = 32.107

A = exp(32.107) = 8.788*10^13