K p = 0·04 atm at 899 K for the equilibrium shown below. What is the equilibrium concentration of C 2 H 6 when it is placed in a flask at 4·0 atm pressure and allowed to come to equilibrium? - Wired Faculty

Question

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K_p = 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?

$straight C subscript 2 straight H subscript 6 left parenthesis straight g right parenthesis space space space rightwards harpoon over leftwards harpoon space space space space straight C subscript 2 straight H subscript 4 left parenthesis straight g right parenthesis space plus space straight H subscript 2 left parenthesis straight g right parenthesis$

Solution

Let at equilibrium,
$straight p subscript straight c subscript 2 straight H subscript 4 end subscript space equals space straight p subscript straight H subscript 2 end subscript space equals space straight p$
The reaction is
$straight C subscript 2 straight H subscript 6 left parenthesis straight g right parenthesis space space rightwards harpoon over leftwards harpoon space space space straight C subscript 2 straight H subscript 4 left parenthesis straight g right parenthesis space plus space straight H subscript 2 left parenthesis straight g right parenthesis$
Initial pressure 4.0 atm 0 0
At equm. 4 - p p p
Applying the law of chemical equilibrium

$straight K subscript straight p space equals space fraction numerator straight p subscript straight C subscript 2 straight H subscript 4 end subscript space cross times space straight p subscript straight H subscript 2 end subscript over denominator straight p subscript straight C subscript 2 straight H subscript 6 end subscript end fraction space space space space space... left parenthesis 1 right parenthesis$
Putting the reaction in expression (1),
we have
$0.04 space equals space fraction numerator straight p squared over denominator 4 minus straight p end fraction or space space space space space straight p squared space equals space 0.16 space minus space 0.04 space straight p or space space space space space straight p squared plus 0.04 straight p space minus space 0.16 space equals space 0 therefore space space space space space straight p space equals space fraction numerator negative 0.04 space plus-or-minus space square root of 0.0016 minus 4 left parenthesis negative 0.16 right parenthesis end root over denominator 2 end fraction space space space space space space space space space space space space space equals space fraction numerator negative 0.04 space plus-or-minus 0.89 over denominator 2 end fraction$
Taking positive value,
$straight p space equals fraction numerator 0.80 over denominator 2 end fraction space equals space 0.40$
$therefore space space space space space space space space space space space space open square brackets straight C subscript 2 straight H subscript 6 close square brackets subscript eq space equals space 4 minus 0.40 space atm space equals space 3.60 space atm$

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Equilibrium

Some More Questions From Equilibrium Chapter

What is equilibrium?

Give two examples of physical equilibrium.

What kind of molecules in a liquid can evaporate?

Name the factors on which vapour pressure of any liquid depends.

Which measurable property becomes constant in water vapour equilibrium?

Give an example from daily life in which there is gas solution equilibrium?

A crystal of common salt of a given mass is kept in its aqueous solution. After 24 hours, its mass remains the same. Is the crystal in equilibrium with the solution?

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