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$N_{2}O_{5}$ decomposes to $NO_{2}$ and $O_{2}$ and follows first order kinetics. After 50 minutes, the pressure inside the vessel increases from 50 mmHg to 87.5 mmHg.
The pressure of the gaseous mixture after 100 minute at constant temperature will be :

Option 1)
175.0 mmHg

Option 2)
116.25 mmHg

Option 3)
136.25 mmHg

Option 4)
106.25 mmHg

Answers (1)

best_answer

As we learned

First Order Reaction -

The rate of the reaction is proportional to the first power of the concentration of the reactant.

- wherein

Formula:

R $\rightarrow$ P

a 0

a-x x

$rate[r]=K[R]^{1}$

$\frac{-d(a-x)}{dt}=K(a-x)$

$\frac{-dx}{dt}=K(a-x)$ [differentiate rate law]

$ln \:[\frac{a}{a-x}]=kt \:(Integrated rate law)$

Unit of $k=sec^{-1}$

$t_\frac{1}{2}=\frac{0.693}{k}$

$N_{2} O_{5} \rightarrow 2NO_{2}+\frac{1}{2}O_{2}$

t=0 50 0 0

t=50min $50-P_{1}$ $2P_{1}$ $\frac{P_{1}}{2}$

=25

t=100min $50-P_{2}$ $2P_{2}$ $\frac{P_{2}}{2}$

12.5

$50-P_{1}$ + $2P_{1}$ + $\frac{P_{1}}{2}$

$\frac{3P_{1}}{2}=37.5$

$P_{1} = \frac{37.5\times 2}{3}=25$

50 minutes is half-life period

for 100 minutes (2 half-life)

$50-P_{2}=12.5$

$P_{2}= 37.5mm$ of Hg

Total Pressure at 100 minutes

$50 - P_{2}+2P_{2}+\frac{P_{2}}{2}$

$50 +\frac{3P_{2}}{2}= 50+\frac{3}{2}\times 37.5$

50+56.25

=106.25mm of Hg

Option 1)

175.0 mmHg

Option 2)

116.25 mmHg

Option 3)

136.25 mmHg

Option 4)

106.25 mmHg

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prateek

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