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Question 20

For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained.

t (sec) P(mm of Hg)
0 35.0
360 54.0
720 63.0

Calculate the rate constant

Answer

The decomposition of azoisopropane to hexane and nitrogen at 543 K is represented by the following equation.

After time, t, total pressure, Pt = (Pº - p) + p + p

⇒ Pt = (Pº + p)

p = P - Pº

therefore, Pº - p = Pº  - P - Pº

= 2 Pº -  Pt

For a first order reaction,

k = 2.303/ Log  Pº / Pº  - p

=   2.303/ 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

When t = 720 s, k = 2.303 / 720s log 35.0 / 2x35.0 - 63.0

= 2.235 × 10 - 3 s - 1

Hence, 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

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