Question

Hi, I'm trying to learn how to use the Arrhenius equation and I am very confused, can someone help? Thank you!

The activation energy for the gas phase decomposition of cyclobutane is 262 kJ/mol.

(CH₂)₄2 C₂H₄

The rate constant for this reaction is 2.16×10^-4 s^-1 at 711 K. What is the rate constant at 749 K?

Use the Arrhenius equation to determine E_a.

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For the gas phase decomposition of cyclobutane, the rate constant is 8.84×10^-4 s^-1 at 734 K and 5.91×10^-3 s^-1 at 768 K.

• (CH₂)₄2 C₂H₄

Calculate the activation energy for this reaction.  kJ/mol

Use Arrhenius plot information to determine E_a.

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The rate of the following reaction was measured at different temperatures and rate constants were determined.

• CH₃CHClCH₂ClCH₃CH=CHCl + HCl

Which of the following should give a linear plot (temperatures in K)?

On the x-axis: _____Tln T1/T   On the y-axis: _____kln k1/k

When the appropriate plot is made, the resulting least-squares line has a slope of -2.77×10⁴ K and a y-intercept of 31.8.

Use this information to determine the activation energy for the reaction.

E_a =  kJ/mol

Answer 1

Arrhenius equation gives dependence of the rate constant on temperature.

Arrhenius equation :

k=Ae^-E_a/RT

k= rate constant

A= pre-exponential factor

E_a =Activation energy

T= temperature

R= universal gas constant

At temperature T₁ the rate of reaction becomes k₁ and at temperature T₂ the rate of reaction becomes k₂.

So, k₁=Ae^-E_a/RT₁

lnk₁ = lnA - E_a/RT₁...................(1)

_and k₂=Ae^-E_a/RT₂

lnk₂ = lnA - E_a/RT₂...................(2)

subtracting (2) from (1)

lnk₁ - lnk₂ = - E_a/RT₁ + E_a/RT₂

ln(k₁ / k₂)= E_a/R(1/ T₂ -1/T₁ )

ln(k₁ / k₂)=E_a/RT₁T₂ (T₁-T₂)

• The rate constant for gas phase decomposition of cyclobutane at 749K is

ln(2.16×10^-4 /k₂)= 262*10³J* (711K-749K) / 8.314 J mol^-1 K^-1 *711K*749K

-8.4402-lnk₂ = 0.05917*(-38)

lnk₂ = -8.4402+2.2486

lnk₂ =-6.1915

k₂ = 2.0467*10^-3

• The activation energy for the reaction is

ln(8.84×10^-4 /5.91×10^-3)=E_a (734K-768K) / 8.314 J mol^-1 K^-1 *734K*768K

-1.8998= Ea (-34) / 4.6867*10⁶

Ea = 272.579 KJ

• lnk₁ = lnA - E_a/RT₁

This equation is like y=mx+c where m= slope and c=intercept

So, the plot of lnk₁ vs 1/T₁ will be linear in nature where y=lnk₁ and x = 1/T₁

slope= - E_a/R and intercept = lnA

- E_a/R =-2.77×10⁴K

E_a= 2.77×10⁴K* 8.314 J mol^-1 K^-1

E_a= 230.2978 KJ mol^-1