The decomposition of formic acid (see below) is measured at several temperatures

Question

The decomposition of formic acid (see below) is measured at several temperatures. The temperature dependence of the first-order rate constant is: Calculate the activation energy, in kJ/mol. Use all data points and do a linear regression using calculator or Excel. Do not pick 2 data points. This is less accurate and assumes all data points are equally good. Answer: Calculate the pre-exponential term (in s^-1) Answer: The activation energy for the isomerization of cyclopropane to propene is 274 kJ/mol. By what factor does the rate of this reaction increase as the temperature rises from 233 to 298 degree C? (The factor is the ratio of the rates.) Answer:

Explanation / Answer

Answer –

Gvien, the first order reaction with rate constant at different temperature

The energy of activation = 127.81 kJ/mol

                                        = 1.278*105 J/mol

Now we need to calculate the pre-exponential term means A in per second

We know Arrhenius equation

k = A.e-Ea/RT

So we can take any one of the rate constant and with respect to temp

0.00027 s-1 = A* e-1.278*105 / 8.314 *800

0.00027 s-1 = A*4.52*10-9

A = 0.00027 s-1 / 4.52*10-9

A = 5.97*104 s-1

So the pre-exponential term is 5.97*104 s-1

Second problem, we are given, Ea = 274 kJ/mol

T1 = 233 +273 = 506 K

T2 = 298 + 273 = 571 K

We know the Arrhenius integrated equation

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

ln (k2/k1) = 2.74*105 J.mol-1 / 8.314 J.mol-1.K-1 * ( 1/571 – 1/506)

ln (k2/k1) = - 32956.5 * (-0.00022)

                 = 7.41

Now we need to take the antiln form both side

(k2/k1) = 1659.5

So the k2 = 1659.5 k1

And this means by the 1659.5 factors the rate of reaction increase as the temp rise form the 233 to 298o C.

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