Ncert Exercises & Solutions

7.17 Kp = 0.04 atm at 899 K for the equilibrium shown below. What is the equilibrium concentration of C2H6 when it is placed in a flask at 4.0 atm pressure and allowed to come to equilibrium?

C2H6 (g) C2H4 (g) + H2 (g)

NEET SOLUTION:

Let p be the pressure exerted by ethene and hydrogen gas (each) at equilibrium. Now, according to the reaction,

$C_{2} H_{6 (g)} \leftrightarrow C_{2} H_{4 (g)} + H_{2 (g)} Initial conc . 4.0 atm 0 0 At equilibrium 4.0 - p p p We can write, \begin{array}{l} \frac{p_{C_{2} H_{4}} \times p_{H_{2}}}{p_{C_{2} H_{6}}} = K_{p} \\ \Rightarrow \frac{p \times p}{40 - p} = 0.04 \\ \Rightarrow p^{2} = 0.16 - 0.04 p \\ \Rightarrow p^{2} + 0.04 p - 0.16 = 0 \\ Now, p = \frac{- 0.04 \pm \sqrt{(0.04)^{2} - 4 \times 1 \times (- 0.16)}}{2 \times 1} \\ = \frac{- 0.04 \pm 0.80}{2} \\ = \frac{0.76}{2} (Taking positive value) \\ = 0.38 \end{array}$

Hence, at equilibrium,

$\begin{array}{l} [C_{2} H_{6}] = 4 - p = 4 - 0.38 \\ = 3.62 atm \end{array}$

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