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Equilibrium

Question
CBSEENCH11006428

1 mole of acetic acid and 1 mole of ethyl alcohol were mixed at 298K. At equilibrium, 0 - 33 mole of acetic acid was found unreacted. Calculate the equilibrium constant for the reaction
            CH subscript 3 COOH plus straight C subscript 2 straight H subscript 5 OH space space rightwards harpoon over leftwards harpoon space space space CH subscript 3 COOC subscript 2 straight H subscript 5 space plus space straight H subscript 2 straight O
Initial  conc.   
1 mole      1 mole            1 mole       0 mole

Equilibrium conc.
0.333      0.333               0 mole        0 mole
             

Solution

Since at equilibrium 0·33 mole of acetic acid is left, we say that 1 – 0·333 = 0·667 mole of acetic acid is used up.
Now according to the equation, it is clear that 0·667 mole of acetic acid combines with a 0·667 mole of ethyl alcohol to form a 0·667 mole of ethyl acetate and a 0·667 mole of water.
At equilibrium [CH3COOH] = 0·333 mole ; [C2H5OH] = 0·333 mole [CH3COOC2H5] = 0·667 mole;
[H2O] = 0·667 mole
Applying the law of chemical equilibrium, we have
straight K subscript straight c space equals space fraction numerator open square brackets CH subscript 3 COOC subscript 2 straight H subscript 5 close square brackets space open square brackets straight H subscript 2 straight O close square brackets over denominator open square brackets CH subscript 3 COOH close square brackets space open square brackets straight C subscript 2 straight H subscript 5 OH close square brackets end fraction
    equals space fraction numerator 0.667 space cross times space 0.667 over denominator 0.333 space cross times space 0.333 end fraction space equals space 4