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# For the reaction ,$N_2O_5(g)\iff 2NO_2(g)+0.5O_2(g)$.Calculate the mole fraction of $N_2O_5(g)$ decomposed at a constant volume and temperature,if the initial pressure at any time is 960mm Hg.Assume ideal gas behaviour.

$(a)\;0.2\qquad(b)\;0.3\qquad(c)\;0.1\qquad(d)\;0.4$

$N_2O_5\iff 2NO(g)+\large\frac{1}{2}$$O_2(g) Initial pressure : N_2O_5\Rightarrow 600 2NO\Rightarrow 0 \large\frac{1}{2}$$O_2\Rightarrow 0$
Final pressure :
$2NO\Rightarrow 600-p$
$2p\Rightarrow 2p$
$\large\frac{1}{2}$$O_2\Rightarrow \large\frac{p}{2} Step 2: p\alpha moles if V,T are constant. \therefore 600-p+2p+\large\frac{p}{2}$$=960$
$p=240mm\;Hg$
$\therefore$ Mole fraction Of $N_2O_5$ decomposed $=\large\frac{240}{600}$
$\Rightarrow 0.4$
Hence (d) is the correct answer.