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

$(C{H}_3{)}_{2}CHN=N(C{H}_3{)}_2⟶N_2+C_6{H}_{14}$

$t=0$ $P_o$ $0$ $0$

at $t=t_f$ $P_o-p$ $p$ $p$

Total pressure at $t=t_f=(P_o-P)+P+P\Rightarrow P_o+P$

$P_t=P_o+P$

$p=P_t-P_o$

For first order reaction,

$K=2.303/t\log \left(\frac{P_o}{P_o-P}\right)\Rightarrow \frac{2.303}{t}\log \left(\frac{P_o}{2P_o-P_t}\right)$

At $t=360s$, $K=2.303/360s\log (35/2\times 35-54)=2.175\times {10}^{-3}{s}^{-1}$

At $t=720s$, $K=2.303/720s\log (35/2\times 35-63)=2.235\times {10}^{-3}{s}^{-1}$

$K=\frac{K_1+K_2}{2}$

$=\frac{(2.175\times {10}^{-3}+2.235\times {10}^{-3})}{2}=2.21\times {10}^{-3}{s}^{-1}$