Question

# Calculate the rate constant, k, for a reaction at 65.0 °C that has an activation energy...

Calculate the rate constant, k, for a reaction at 65.0 °C that has an activation energy of 87.1 kJ/mol and a frequency factor of 8.62 × 1011 s–1.

Step 1: Explanation:

Activation Energy can be calculated from the Arrhenius equation

k=Ae−Ea/RT

Where,

k = Rate constant, A = Frequency factor , Ea = Activation energy, R = Gas constant

T = Absolute Temperature

Step 2: Extract the data from question

k = we need to calculate

A = 8.62 × 1011 s-1

Ea = 87.1 kJ/mol = 87100 kJ/mol

[ Note: 1 kJ = 1000 J =>  ( 87.1 kJ/mol   × 1000 J / 1 kJ ) = 87100 J/mol

R = 8.314 J / mol.K

T = 65°C = (65+273.15)K = 338.15 K

Step 3: Calculation of Rate constant

k=Ae−Ea/RT

By substituting the above value

=> k = 8.62 × 1011 s-1 × e-(87100 J/mol ) / (8.314 J/mol.K × 338.15 K)

=? k => 0.03024 s-1 ≈ 3× 10-2 s-1

hence, the rate constant for the reaction at 65 °C = 0.03024 s-1 ≈ 3× 10-2 s-1

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