Question

The following data were obtained during the first order thermal decomposition of $N_2O_5{(g)} $ at constant volume
$ 2N_2 O_5{(g)} \to 2N_2O_4{(g)} + O_2{(g)} $

The rate constant is

• A. $2 \times 10^{-4} s^{-1} $
• B. $5 \times 10^{-4} s^{-1} $
• C. $3 \times 10^{-4} s^{-1} $
• D. $8 \times 10^{-4} s^{-1} $

Answer 1

Answer: (B)

$\begin{matrix}&2N_{2}O_{5\left(g\right)}&\to&2N_{2O_{4\left(g\right)}}+&O_{2\left(g\right)}\\
t=0&0.5 atm&&&\\ t=t&\left(0.5 - 2x\right)atm&&2x atm&x atm\end{matrix}$
$ p_{t}=p_{N_{2O4}} +P_{o2} $
$ x=P_{t}- 0.5
P_{N_2O_5}=0.5 -2x $
$ 0.5 -2\left(P_{t}-0.5\right)=1.5-2P_{t } $
$At t =100s;p_{t }=0.512 atm $
$ P_{N_2O_5}=1.5-2\times0.512 =0.476 atm $
$k=\frac{2.303}{t}log \frac{Pi}{PA} =\frac{2.303}{100s } log\frac{ 0.5 atm}{0.476 atm } $
$=\frac{2.303}{100s} \times0.0216 =4.98\times10^{-4}s^{-1}$