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Derivation of Kp and Kc

A mixture of ...

Question

A mixture of two moles of $N_{2}$ and 8 moles of $H_{2}$ are heated in a 2 lit vessel. At equilibrium, 0.4 moles of $N_{2}$ was observed, the equilibrium concentration of $H_{2}$ was.

A

2M

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B

4M

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C

1.6M

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D

1M

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Solution

The correct option is C 1.6M
The equilibrium reaction is $N_{2} (g) + 3 H_{2} (g) \Leftrightarrow 2 N H_{3} (g)$ .
Following table list the number of moles of various species.

$N_{2}$
$H_{2}$
Initial
2
8
Change
-x
-3x
Equilibrium
2-x
8-3x
At equilibrium, the number of moles of nitrogen is $2 - x = 0.4$ or $x = 1.6$ .
Hence at equilibrium number of moles of hydrogen are $8 - 3 x = 8 - 3 (1.6) = 3.2$ .
Thus 3.2 moles of hydrogen are present in 2 L.
Hence, equilibrium concentration of hydrogen is $\frac{3.2}{2} = 1.6 M$ .

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