Nitrogen pentoxide decomposes according to equation: 2N_ 2 O_ 5 (… - Vidyadip

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 $(min)$
$0.400$	$0.00$
$0.289$	$20.0$
$0.209$	$40.0$
$0.151$	$60.0$
$0.109$	$80.0$

Calculate the rate constant. Include units with your answer.
What will be the concentration of $N_2O_5$ after $100$ minutes?
Calculate the initial rate of reaction.

✓

Answer

$\text{k}=\frac{2.303}{t}\log\frac{[A_{o}]}{[A]}$

$\text{k}=\frac{2.303}{\text{20 min}}\log\frac{0.400}{0.289}$
$\text{k} = 0.0163\text{ min}^{–1}$

$\text{k}=\frac{2.303}{\text{t}}\log\frac{[A_o]}{[A]}$

$\text{0.0163}=\frac{2.303}{\text{100}}\log\frac{0.400}{[A]}$
$[\text{A}] = 0.078\text{M}$

$\text{Initial rate R = k}[\text{N}_2\text{O}_5]$

$= 0.0163\text{ min}^{–1} \times (0.400\text{ M})$
$= 0.00652\text{M min}^{–1}.$

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