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Question

$$\displaystyle { K }_{ p }=0.04\;atm$$ at 899 K for the equilibrium shown below. What is the equilibrium concentration of $$\displaystyle { C }_{ 2 }{ H }_{ 6 }$$ when it is placed in a flask at 4.0 atm pressure and allowed to come to equilibrium?
$$\displaystyle { C }_{ 2 }{ H }_{ 6 }\left( g \right) \rightleftharpoons { C }_{ 2 }{ H }_{ 4 }\left( g \right) +{ H }_{ 2 }\left( g \right) $$


Solution

The initial partial pressures of ethane, ethylene and hydrogen are 4.0 atm, 0 atm and 0 atm respectively.
The equilibrium parial pressures are 4-p atm, p atm and p atm respectively.
The equilibrium constant expression is
$$\displaystyle K_c =\frac{P_{C_2H_4}P_{H_2}}{P_{C_2H_6}} = \frac {p \times p} {4-p} = 0.04$$
$$\displaystyle p^2 = 0.16 - 0.04p $$
$$\displaystyle p = 0.38 $$
The equilibrium concentration of ethane is $$\displaystyle   4 - 0.38 = 3.62 \ atm$$.

Chemistry
NCERT
Standard XI

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