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Introduction to Le Chatelier's Principle

A mixture of ...

Question

A mixture of $S O_{3}, S O_{2}$ and $O_{2}$ gases are maintained at equilibrium in 10 litre flask at a temperature at which $K_{c}$ for the reaction, $2 S O_{2} (g) + O_{2} (g) \Leftrightarrow 2 S O_{3} (g)$ is 100 $m o l^{- 1}$ litre. At equilibrium,

a) If no of mole of $S O_{3}$ and $S O_{2}$ in the flask are same, how many moles of $O_{2}$ are present?
b) If no. of mole of $S O_{3}$ in the flask are twice the no of mole of $S O_{2}$ , how many moles of $O_{2}$ are present?

A

0.1 and 0.4

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B

0.5 and 0.7

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C

0.8 and 0.4

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D

0.1 and 4

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Solution

The correct option is A 0.1 and 0.4
The equilibrium reaction is $2 S O_{2} (g) + O_{2} (g) \Leftrightarrow 2 S O_{3} (g)$ .
The number of moles of $S O_{2}$ and $S O_{3}$ are same. Hence, their molar concentration is also same.
The expression for the equilibrium constant is $K_{c} = \frac{[S O_{3}]^{2}}{[S O_{2}]^{2} [O_{2}]}$
Substitute values in the above expression:
$100 = \frac{1}{[O_{2}]}$
Thus, $[O_{2}] = 0.01 M$

1 L contains 0.01 moles of oxygen.
10 L will contain 0.1 moles of oxygen.

(b) The number of moles of $S O_{3}$ is twice the number of moles of $S O_{2}$ $. H e n c e, t h e i r m o l a r c o n c e n t r a t i o n i s a l s o i n t h e s a m e r a t i o . T h e e x p r e s s i o n f o r t h e e q u i l i b r i u m c o n s t a n t i s$ K_c= \dfrac {[SO_3]^2}{[SO_2]^2[O_2]} $S u b s t i t u t e v a l u e s i n t h e a b o v e e x p r e s s i o n :$ 100=\dfrac {4}{[O_2]} $T h u s$ [O_2] = 0.04M$

1 L contains 0.04 moles of oxygen.
10 L will contain 0.4 moles of oxygen.

Hence, option A is correct.

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Similar questions

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2 S O_{2} (g) + O_{2} (g) ⇌ 2 S O_{3} (g)

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