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Equilibrium

Question
CBSEENCH11006425

Ethyl acetate, is formed by the reaction of ethanol and acetic acid and equilibrium is represented as
CH subscript 3 COOH left parenthesis straight l right parenthesis space plus space straight C subscript 2 straight H subscript 5 OH left parenthesis straight l right parenthesis space space rightwards harpoon over leftwards harpoon space space space CH subscript 3 COO subscript 2 straight H subscript 5 left parenthesis straight l right parenthesis space plus space straight H subscript 2 straight O left parenthesis straight l right parenthesis
(i) Write the concentration ratio (reaction quotient), Qc, for this reaction (note:water is not in excess and is not a solvent in this reaction).
(ii) At 293K, if one starts with 1·00 mol of acetic acid and 0·18 mol of ethanol, there is 0·171 mol of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant.
(iii) Starting with 0·5 mole of ethanol and 1·0 mole of acetic acid and maintaining it at 293K, 0·214 mole of ethyl acetate is formed after sometime. Has equilibrium been reached ?

Solution
(i) The various molar concentrations before the reaction and at equilibrium point may e represented as
       CH subscript 3 COOH left parenthesis straight l right parenthesis space plus space straight C subscript 2 straight H subscript 5 OH space left parenthesis straight l right parenthesis rightwards harpoon over leftwards harpoon space space CH subscript 2 COO subscript 2 straight H subscript 5 left parenthesis straight l right parenthesis space plus space straight H subscript 2 straight O left parenthesis straight l right parenthesis
The concentration ratio Q for this reaction is given by,
straight Q subscript straight C space equals space fraction numerator open square brackets CH subscript 3 COOC subscript 2 straight H subscript 5 left parenthesis straight l right parenthesis close square brackets space open square brackets straight H subscript 2 straight O left parenthesis straight l right parenthesis close square brackets over denominator open square brackets CH subscript 3 COOH left parenthesis straight l right parenthesis close square brackets space open square brackets straight C subscript 2 straight H subscript 5 OH left parenthesis straight l right parenthesis close square brackets end fraction

(ii) The various molar concentrations before the chemical reaction and at equilibrium point may be represented as
                CH subscript 3 COOH left parenthesis l right parenthesis space plus space straight C subscript 2 straight H subscript 5 OH left parenthesis l right parenthesis space space rightwards harpoon over leftwards harpoon space space CH subscript 3 COOC subscript 2 straight H subscript 5 left parenthesis l right parenthesis space plus space straight H subscript 2 straight O left parenthesis l right parenthesis
Initialconc.          
1 mole          0.180 ml         0                         0
Equilibrium conc.          
1 - 0.171    0.180 - 0.171  = 0.171         0.171 
 (0.829)         (0.009)      = 0.171         0.171
Applying the law of chemical equilibrium,
       straight K subscript straight c space equals space fraction numerator open square brackets CH subscript 3 COOC subscript 2 straight H subscript 5 left parenthesis straight l right parenthesis close square brackets space open square brackets straight H subscript 2 straight O left parenthesis straight l right parenthesis close square brackets over denominator open square brackets CH subscript 3 COOH left parenthesis straight l right parenthesis close square brackets space open square brackets straight C subscript 2 straight H subscript 5 OH left parenthesis straight l right parenthesis close square brackets end fraction
space space space space equals space fraction numerator 0.171 space cross times space 0.171 over denominator 0.829 space cross times space 0.009 end fraction space equals 3.91
(iii) The various molar concentrations before the reaction and at equilibrium point may be represented as
                       CH subscript 3 COOH left parenthesis straight l right parenthesis space plus space straight C subscript 2 straight H subscript 5 OH left parenthesis straight l right parenthesis space rightwards harpoon over leftwards harpoon space space space CH subscript 2 COO subscript 2 straight H subscript 5 left parenthesis straight l right parenthesis space plus space straight H subscript 2 straight O left parenthesis straight l right parenthesis
Initial conc.        
1.00 mole           0.5 mole     0                       0
Equilibrium conc.         
1 - 0.214        0.5- 0.214    =   0.214          0.214
                  
(0.786)            (0.286)      =   0.214          0.214
Concentration ratio,
               straight Q subscript straight c space equals space fraction numerator open square brackets CH subscript 3 COOC subscript 2 straight H subscript 5 left parenthesis straight l right parenthesis close square brackets space open square brackets straight H subscript 2 straight O left parenthesis straight l right parenthesis close square brackets over denominator open square brackets CH subscript 3 COOH left parenthesis straight l right parenthesis close square brackets space open square brackets straight C subscript 2 straight H subscript 5 OH left parenthesis straight l right parenthesis close square brackets end fraction
equals space fraction numerator 0.214 space cross times space 0.214 over denominator 0.786 space cross times space 0.286 end fraction space equals space 0.204
As the value of Qc is less than the value of equilibrium constant, therefore, the equilibrium has not reached.