The decomposition of O_{3(g)} follows first o | vedclass

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(C) The decomposition reaction is $O_{3(g)} \longrightarrow O_{2(g)} + O_{(g)}$.Initial pressure: $100 \ atm, \ 0, \ 0$.Pressure after time $t$: $(100

Vedclass · Accepted Answer

$10, 90, 90$

Vedclass · Answer

(C) The decomposition reaction is $O_{3(g)} \longrightarrow O_{2(g)} + O_{(g)}$.Initial pressure: $100 \ atm, \ 0, \ 0$.Pressure after time $t$: $(100-x), \ x, \ x$.Given: $k = 1.0 	imes 10^{-3} \ s^{-1}$,$t = 38.38 \ min = 38.38 	imes 60 \ s = 2302.8 \ s$.Using the first-order rate equation: $k = \frac{2.303}{t} \log \frac{p_i}{p_f}$.$1.0 	imes 10^{-3} = \frac{2.303}{2302.8} \log \frac{100}{100-x}$.$\log \frac{100}{100-x} = \frac{1.0 	imes 10^{-3} 	imes 2302.8}{2.303} \approx 1$.$\frac{100}{100-x} = 10^1 = 10$.$100 = 1000 - 10x \implies 10x = 900 \implies x = 90 \ atm$.Partial pressure of $O_3 = 100 - 90 = 10 \ atm$.Partial pressure of $O_2 = 90 \ atm$.Partial pressure of $O = 90 \ atm$.Thus,the correct option is $C$.

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