Question

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 1

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

                         $(CH_3)_2CHN=NCH(CH_3)_2(g)→N_2(g)+C_6H_{14}(g)$  

At t = 0 P0 0 0
At t = 0 P0 - p p p
Pt = (P0 - p) + p + p
After time t, total pressure
⇒ Pt = P0 + p
⇒ p = Pt - P0
Therefore, P0 - P = P0 - (Pt - P0)
= 2P0 - Pt
For a first order reaction,

$k = \frac {2.303}{t} log \ \frac {P_0}{P_0-p}$

$k = \frac {2.303}{t} log\ \frac {P_0}{2P_0-p_t}$

$When\ t = 360\ s$

$k = \frac {2.303}{360\ s} log\ \frac {35.0}{2\times 35.0-5.0}$

$k = 2.175 \times 10^{-3} s^{-1}$

$When\ t = 720\ s$

$k = \frac {2.303}{720\ s} log\ \frac {35.0}{2\times 35.0-63.0}$

$k = 2.235 \times 10^{-3} s^{-1}$

Hence the average value of rate constant is

$k =\frac { (2.175 \times 10^{-3}) + (2.235 \times 10^{-3})}{2} s^{-1}$

$k = 2.21\times 10^{-3} s^{-1}$