Question
Nitrogen pentoxide decomposes according to equation: $\text{2N}_{2}\text{O}_{5}\text{(g)}\rightarrow\text{4NO}_{2}\text{(g)}+\text{O}_{2}\text{(g)}.$
This first order reactionwas allowed to proceed at $40^\circ C$ and the data below were collected:
$[N_2O_5](M)$ Time $(min)$
$0.400$ $0.00$
$0.289$ $20.0$
$0.209$ $40.0$
$0.151$ $60.0$
$0.109$ $80.0$
  1. Calculate the rate constant. Include units with your answer.
  2. What will be the concentration of $N_2O_5 $ after $100$ minutes?
  3. Calculate the initial rate of reaction.

Answer

  1. $\text{k}=\frac{2.303}{t}\log\frac{[A_{o}]}{[A]}$
$\text{k}=\frac{2.303}{\text{20 min}}\log\frac{0.400}{0.289}$
$\text{k} = 0.0163\text{ min}^{–1}$
  1. $\text{k}=\frac{2.303}{\text{t}}\log\frac{[A_o]}{[A]}$
$\text{0.0163}=\frac{2.303}{\text{100}}\log\frac{0.400}{[A]}$
$[\text{A}] = 0.078\text{M}$
  1. $\text{Initial rate R = k}[\text{N}_2\text{O}_5]$
$= 0.0163\text{ min}^{–1} \times (0.400\text{ M})$
$= 0.00652\text{M min}^{–1}.$

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