$C_{2} H_{5} C l (g) \to C_{2} H_{4} (g) + H C l (g)$
Time(sec.) Total pressure (atm)
$0$ $0.30$
$300$ $0.50$
For the first order thermal decomposition reaction, the following data was obtained.
Calculate the rate constant.

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Solution

given, Initial pressure
$P_{0} = 0.30 a t m$
$P_{t} = 0.50 a t m$
$t = 300 s$
Rate constant, $K = \frac{2.303}{t} l o g \frac{P_{0}}{{2 P}_{0} - P_{t}}$

$= \frac{2.303}{300} l o g \frac{0.30}{2 \times 0.30 - 0.50}$

$= \frac{2.303}{300} l o g \frac{0.30}{0.60 - 0.50}$

$= \frac{2.303}{300} l o g \frac{0.30}{0.10}$

$= \frac{2.303}{300} l o g 3$

$= \frac{2.303}{300} \times 0.4771$

$= 3.66 \times 10^{- 3} s^{- 1}$

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