An unusual atmospheric reaction leading to ozone destruction is CF 3 O + O 3 CF

Question

An unusual atmospheric reaction leading to ozone destruction is CF3O + O3 CF3O2 + O2, the analysis of which has yielded an Arrhenius frequency factor (A) and activation energy of 2.0 × 10–12 cm3 molecule–1 s–1 and 11.6 kJ/mol, respectively. Calculate the rate constant for this reaction at an altitude of 35 km, where the temperature is –34°C. Please show detailed work.

2.0 × 10–12 M–1 s–1

1.2 × 109 M–1 s–1

3.5 × 106 M–1 s–1

7.9 × 10–15 M–1 s–1

6.8 × 108 M–1 s–1

2.0 × 10–12 M–1 s–1

1.2 × 109 M–1 s–1

3.5 × 106 M–1 s–1

7.9 × 10–15 M–1 s–1

6.8 × 108 M–1 s–1

Explanation / Answer

Given that

activation energy Ea = 11.6 kJ/mol = 11600 J/mol

frequency factor A = 2.0 x 10-12 cm3 molecule-1 s-1

                          = 2.0 x 10-12 x 0.001 L x (6.022 x 1023 mol-1) x s-1

                          = 12.044 x 108 L mol-1 s-1

                          = 12.044 x 108 M-1 s-1

temperature T = -34 C = -34 + 273 K = 239 K

Arrhenius equation is

k = A e-Ea/RT , k = rate constant

R = 8.314 J/K/mol

Then,

  k = A e-Ea/RT

= (12.044 x 108 M-1 s-1) e[(- 11600 J/mol) /(8.314 J/K/mol) (239K)]

    = 3.5 x 106 M-1 s-1

k = 3.5 x 106 M-1 s-1

Therefore,

the rate constant of the reaction at -34C = 3.5 x 106 M-1 s-1

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