The reaction shown in the equation is second order overall. The value of k, the

Question

The reaction shown in the equation is second order overall. The value of k, the specific rate constant, was measured at several temperatures. Determine the activation energy for this reaction using the data shown below.

C2H5Br(aq) + OH– (aq) C2H5OH(aq) + Br–(aq)

Temp (oC)

K, L mol-1s-1

25.1

8.76 x 10-5

30.0

1.63 x 10-4

34.9

2.80 x 10-4

40.2

4.97 x 10-4

45.2

8.63 x 10-4

49.8

1.44 x 10-3

Temp (oC)

K, L mol-1s-1

25.1

8.76 x 10-5

30.0

1.63 x 10-4

34.9

2.80 x 10-4

40.2

4.97 x 10-4

45.2

8.63 x 10-4

49.8

1.44 x 10-3

Explanation / Answer

Given :

Lets use any of the two temperature to calculate activation energy.

We use Arrhenius equation,

ln K2 /K1 = -Ea/ R ( 1/T2 – 1/ T1)

Here k2 and k1 are the rate constant at Temperature T2 and T1 respectively.

Ea is activation energy, R is gas constant = 8.314 J / (K.mol)

Let, T1 = 40.2 deg C , k1 = 4.97 E-4 L / (mol . s)

And T2 = 45.2 deg C , k2 = 8.63 E-4 L/ (mol. s)

Conversion of Temperature to K

T1 = 40.2 deg C + 273.15 = 313.35 K

T2 = 45.2 deg C +273.15 = 318.35

Lets use these value to calculate Ea.

Ln ( 8.63 E-4 / 4.97E-4 ) = - Ea / 8.314 J / (K.mol) [ 1/318.35 K - 1/ 313.35 K]

0.5518 = - Ea / 8.314 J / (K.mol) [ 5.01 E-5 K-1 ]

Lets rearrange this equation

Ea = 91532 J

Ea = 91.532 kJ

The answer is close to 90.1 kJ

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