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Rate of Reaction

The following...

Question

The following data in the table were obtained during the first order thermal decomposition of $S O_{2} {C l}_{2}$ at a constant volume:
$S O_{2} {C l}_{2} (g) ⟶ S O_{2} (g) + {C l}_{2} (g)$
Calculate the rate constant.
(Given: $log 4 = 0.6021, log 2 = 0.3010$ )

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Solution

The thermal decomposition of $S O_{2} C l_{2}$ at a constant volume is represent by the following reaction.
$\begin{matrix} S O_{2} C l_{2 (g)} & \to & S O_{2 (g)} & + & C l_{2 (g)} A t t = 0 & P_{0} & 0 & 0 A t t = t & P_{0} - p & p & p \end{matrix}$
After time t, total pressure, $P_{t} = (P_{0} - p) + p + p$
$P_{t} = P_{0} + p$
which on rearrangement gives:
$p = P_{t} - P_{0}$
Therefore, $P_{o} - p = P_{o} - (P_{t} - P_{o})$
$= 2 P_{o} - P_{t}$
For a first-order reaction,
$k = \frac{2.303}{t} l o g \frac{P_{o}}{2 P_{o} - P_{t}}$
$= \frac{2.303}{100} l o g \frac{0.4}{0.1}$
$= 1.38 \times 10^{- 2} s^{- 1}$

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