Question

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?

Answer #1

**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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