Question

For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained.
t(sec)
0
360
720

P(mm of Hg)
35.0
54.0
63.0
Calculate the rate constant.

Answer 1

The solution of the given problem is following – After time, t, total pressure, Pt = (Pº - p) + p + p ⇒ Pt = (Pº + p) ⇒ p = Pt  - Pº.

Therefore we can write, Pº - p = Pº  - Pt  - Pº = 2 Pº -  Pt. For the first order reaction, k = 2.303/t  Log  Pº / Pº  - p =   2.303/t  Log  Pº / 2 Pº  -  Pt.

When t = 360 s, k = 2.303 / 360s log 35.0 / 2x35.0 - 54.0 = 2.175 × 10 - 3 s – 1.

On the other hand, when t = 720 s, k = 2.303 / 720s log 35.0 / 2x35.0 - 63.0 = 2.235 × 10 - 3 s – 1.

The average value of rate constant is k = (2.175 × 10 - 3  + 2.235 × 10 - 3 ) / 2   s – 1 = 2.21 × 10 - 3 s – 1.