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.
The decomposition of azoisopropane to hexane and nitrogen at 543 K is represented by the following equation.
(CH3)2CHN = NCH(CH3)2(g) → N2(g) + C6H14(g)
At t = 0 P0 0 0
At t = t P0 - p p p
After time, t, total pressure,
Pt = (P0 - p) + p + p
⇒Pt = P0 - p
⇒ p = Pt - P0
Therefore, P0 - p = P0 - (Pt - P0)
= 2Pt - P0
For a first order reaction,
k = \(\frac{2.303}{t}\)log \(\frac{P_0}{P_0 - p}\)
= \(\frac{2.303}{t}\)log \(\frac{P_0}{2P_0 - P_t}\)
When t = 360 s,
k = \(\frac{2.303}{360 s}\)log k = \(\frac{35.0}{2 \times 35.0 - 54.0}\)
= 2.175 × 10-3 s-1
When t = 720 s,
k = \(\frac{2.303}{720 s}\)log k = \(\frac{35.0}{2 \times 35.0 - 63.0}\)
= 2.235 × 10-3 s-1
Hence, the average value of rate constant is
k = \(\frac{(2.175 \times 10^{-3})+(2.235 \times 10^{-3})}{2}s^{-1}\)
= 2.21 × 10-3 s-1