The following data were obtained during first order thermal decomposition of $N_{2} O_{3} (g)$ at constant volume:
$2 N_{2} O_{3} (g) ⟶ 2 N_{2} O_{4} (g) + O_{2} (g)$
S.No Time (s) Total Pressure (atm)
1 0 0.5
2 100 0.512
Calculate the rate constant.

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Solution

$2 N_{2} O_{3} (g) ⟶ 2 N_{2} O_{4} (g) + O_{2} (g)$

$t = 0$ $0.5$ $0$ $0$
$t = 100$ $0.5 - 2 x$ $2 x$ $x$

At $t = 100 s$ , total pressure is $0.512 a t m$

$∴ 0.5 - 2 x + 2 x + x = 0.512$

$0.5 + x = 0.512$

$x = 0.012 a t m$

$P (N_{2} O_{5})$ at $t = 100 = 0.476 a t m$

Now using first order equation, $k t = l n (\frac{a_{o}}{a_{o} - x})$

$k \times 100 = l n (\frac{0.5}{0.476})$

$k = 4.91 \times 10^{- 4} s^{- 1}$

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Similar questions

N_{2} O_{5} (g)

2 N_{2} O_{5} (g) \to 2 N_{2} O_{4} (g) + O_{2} (g)

Time (s)	0	100
Total pressure (atm)	0.5	0.512

S O_{2} C l_{2}

S O_{2} C l_{2} (g) \to S O_{2} (g) + C l_{2} (g)

S O_{2} {C l}_{2}

S O_{2} C l (g) ⟶ S O_{2} (g) + {C l}_{2} (g)

log 4 = 0.6021, log 2 = 0.3010

S O_{2} C l_{2}

S O_{2} C l_{2 (g)} \to S O_{2 (g)} + C l_{2 (g)}

S O_{2} {C l}_{2}

S O_{2} {C l}_{2} (g) ⟶ S O_{2} (g) + {C l}_{2} (g)

log 4 = 0.6021, log 2 = 0.3010

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