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First Order Reaction

The half life...

Question

The half life or the reaction $N_{2} O_{5} = 2 {N O}_{2} + \frac{1}{2} O_{2}$ in 24 hrs at $30^{0}$ . Starting with 10g of $N_{2} O_{5}$ . How many grams of $N_{2} O_{5}$ will remain after a period of 96 hrs?

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Solution

Decomposition of $N_{2} O_{5}$ has a half-life of 24 hours
96 hours $= 4 \times t_{1 / 2}$
Therefore if we start with 10g $N_{2} O_{5} .$ We will have $\frac{10}{2^{4}} g$ after 96 hours
$= \frac{10}{16} = 0.6250 g$
After 96 hours, 0.6250 g of $N_{2} O_{5}$ will remains.

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