682 Chapter 13 | Chemical Kinetics 13.98 The conversion of cyclopropane, an anes

Question

682 Chapter 13 | Chemical Kinetics 13.98 The conversion of cyclopropane, an anesthetic, to propyl- 3.99 h ene (see Problem 13.68) has a rate constant k = 1.3 × 10-6 s-1 at 673 Kand1.1 × 10-5s-1 at 703 K. What is the activation energy in kJ/mol? Use the data given at 703 K to calculate the frequency factor, A, for this reac 13.1 tion. What is the rate constant for the reaction at 350 °C? 3.99 The decomposition of N2O, has an activation energy of 103 kJ/mol and a frequency factor of 4.3 × 1013 s-1 What is the rate constant for this decomposition at (a) 25 °C and (b) 373 K? .100 At 35 °C, the rate constant for the reaction 13.10 121 22 11 sucrose

Explanation / Answer

Answer - We are given, T1 = 673 K , T2 =703 K

k1 = 1.3*10-6 s-1 , k2 = 1.1*10-5 s-1

Ea = ?

The intergraded Arrhenius equation

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

ln 1.3*10-6 / 1.1*10-5 = Ea/ 8.314 J/mol.K * (1/703 – 1/673 K)

-2.13 = Ea/ 8.314 J/mol.K * -6.34*10-5

So, Ea = -2.90 * 8.314 J/mol.K / -6.34*10-5

             = 2.80*105 J/mol

             = 280 kJ/mol

Now pre-exponential factor A for this reaction

T = 703 K , k = 1.1*10-5 s-1

Ea = 2.80*105 J. mol-1

We know Arrhenius equation

k = Ae-Ea/RT

1.1*10-5 s-1 = A * e-(280000 J. mol-1/8.314 *703)

1.1*10-5 s-1 = A * 1.56*10-21

So, A = 1.13*10-5 s-1 / 3.14*10-5

        = 7.03*1015 s-1

Now we are given, T1 = 673 K , T2 = 350+273.15 = 623.15 K

k1 = 1.3*10-6 s-1 , k2 = ?

Ea = 2.80*105 J/mol

The intergraded Arrhenius equation

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

ln 1.3*10-6 / k2 = 2.80*105 J. mol-1 / 8.314 J/mol.K * (1/623.15 – 1/673)

ln 1.3*10-6 / k2 = 0.00569

so taking anitln from both side

3.27*10-6 / k2 = 1.0057

So, k2 = 1.3*10-6 / 1.0057

           = 1.29*10-6 s-1

13.99 ) We are given, Ea = 103 kJ/*mol

A = 4.3*1013 s-1

a)T = 25+273 = 298

We know Arrhenius equation

k = Ae-Ea/RT

k = 4.3*1013 s-1* e-(103000J. mol-1/8.314 *298)

k = 3.8*10-5 s-1

b)T = 373

We know Arrhenius equation

k = Ae-Ea/RT

k = 4.3*1013 s-1* e-(103000J. mol-1/8.314 *373)

k = 0.162 s-1

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