First slide

Kinetics of chemical reactions

Question

The half time of first order decomposition of nitramide is 2.1 hour at 15°C.
${NH}_{2} {NO}_{2} (aq .) \overset{}{\to} N_{2} O (g) + H_{2} O (l)$
If 6.2 g of $N H_{2} N O_{2}$ is allowed to decompose, calculate time taken in hours for $N H_{2} N O_{2}$ to decompose 99%. $[\log_{10} 2 = 0.3]$

Moderate

Solution

$∵$ $t = \frac{2.303}{k} \log_{10} \frac{a}{(a - x)}$
$If t = \frac{t}{2}, x = \frac{a}{2}; ∴ t_{1 / 2} = \frac{2.303}{k} \log_{10} \frac{a}{a - \frac{a}{2}} . . . . . (1)$
If $t = t_{99 %}, x = \frac{99 a}{100}; t_{99 %} = \frac{2.303}{k} \log_{10} \frac{a}{a - \frac{99 a}{100}} . . . . (2)$
By Eqs. (1) and (2),
$t_{99 %} = \frac{\log_{10} 100}{\log_{10} 2} \times t_{1 / 2} = \frac{2}{0.3010} \times 2.1 = 13.95 h o u r$

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