Question

# Benzene diazonium chloride, C6H5NNCl, decomposes fallowing a first order rate law. C6H5NNCl→ C6H5 Cl+N2 If the...

Benzene diazonium chloride, C6H5NNCl, decomposes fallowing a first order rate law.

C6H5NNCl→ C6H5 Cl+N2

If the rate constant at 20°C is 4.3 x 〖10〗^(-5)/s. How long would it take for 83% of the compound to decompose? If the rate constant is 9.0 x 〖10〗^(-4) at 55°C what will the activation energy be?

given a first order reaction

we know that

ln A = ln Ao - kt

ln (Ao/A) = kt

given

83 % of the compound is decomposed

so

17% remains

so

A = 0.17 Ao

k = 4.3 x 10-5

so

ln ( 1/0.17) = 4.3 x 10-5 x t

t = 41208 s

so

it would take 41208 seconds for 83% of the compound to decompose

now

we know that

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

given

k1 = 4.3 x 10-5

T1 = 293

k2 = 9 x 10-4

T2 = 328

so

ln ( 9 x 10-4 / 4.3 x 10-5) = ( Ea / 8.314) ( 1/ 293 - 1/328)

so

Ea = 69.427 x 10^3 J/mol

so

the activation energy is 69.427 kJ/mol

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