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Question

Values of the rate constant for the decomposition of N₂O₅ at four different temperatures are as follows:

T (K): k (M^-1s^-1):

658 2.14 x 10⁵

673 3.23 x 10⁵

688 703 x 10⁵

Determine the activation energy of the decomposition reaction.

____ kJ/mol

Calculate the rate constant of the reaction at 300 K.

______ M^-1s^-1

Can someone please help me answer this problem?

Answer 1

You can do this just like your previous question where you plot ln k vs 1/T (Arrhenius plot) where the slope of the line = -Ea/R. Then solve for Ea. Another way to do it is to use the Arrhenius equation and solve for Ea. I'll show you the latter procedure below as I can't plot the data on this platform.

We can use the equation ln(k2/k1) = -Ea/R (1/T2 - 1/T1)

k1 = 2.14x10⁵

k2 = 3.23x10⁵

T1 = 658K

T2 = 673K

R = 0.008314 kJ/K-mol

Ea = ?

ln (3.23x10⁵/2.14x10⁵) = -Ea/0.008314 (1/673 - 1/658)

0.412 = -Ea/0.008314 (0.00149 - 0.00152)

0.412 = +0.00003 Ea / 0.008314

Ea = 114 kJ/mole

(please be sure to check the math)

To find the rate constant at 300K, use the same equation and solve for k2.

ln (k2/k1) = -Ea/R (1/T2 - 1/T1)

k1 = 2.14x105

k2 = ?

Ea = 114 kJ/mol

R = 0.008314 kJ/K-mol

T1 = 658K

T2 = 300K

Plug in the values and solve for k2