Question

For the first order thermal decomposition reaction, the following data were obtained:
$C_2{H}_{5}C{l}_{\left(g\right)}\stackrel{hv}{\to }{C}_2{H}_{4\left(g\right)}+HC{l}_{\left(g\right)}$
Time (sec) Total pressure (atm)
0 0.30
300 0.50
Calculate the rate constant.(Given: log 2 = 0.301, log3 = 0.4771, log 4 = 0.6021)

Answer 1

$C_2{H}_{5}Cl\left(g\right)\stackrel{h\nu }{\to }{C}_2{H}_4\left(g\right)+HCl\left(g\right)$

$\begin{array}{cccccccccc}Att=0& P_o& & & 0& & & & & 0\\ Att=t& P_o-p& & & p& & & & & p\end{array}$

After time t, total pressure, $P_t=(P_o-p)+p+p$

$\Rightarrow P_t=(P_o+p)$

$\Rightarrow p=P_t-P_o$

Therefore, $P_o-p=P_o-P_t+Po$

$=2P_o-P_t$

For a first order reaction,

$k=\frac{2.303}{t}log\left(\frac{P_o}{P_o-p}\right)$

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

At $t=300,p_t=0.5,p_0=0.3$

So, $k=3.6\times {10}^{-3}se{c}^{-1}$