Question
For the first order thermal decomposition reaction, following data were obtained:
$C_2H_5Cl(g)$ $\xrightarrow{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }}$ $C_2H_4(g) + HCl(g)$
Time/sec   Total pressure/atm
0   0.30
300   0.50
Calculate the rate constant.
(Given : log 2 = 0.301, log 3 = 0.4771, log 4 = 0.6021)

Answer

$\text{k}=\frac{2.303}{\text{t}}\text { }\log\text{ }\frac{\text{p}_{\text{i}}}{2\text{p}_{\text{i}}-\text{p}_{\text{t}}}$
$=\frac{2.303}{300}\text{ }\log\text{ }\frac{0.3}{2\times0.3-0.5}$
$=\frac{2.303}{300}\text{ }\log\text{ }3$
$=\frac{2.303\times0.4771}{300}$
$= 0.0036\ atm^{-1}$ or $0.004\ atm^{-1}$ (approx.)

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