The ester , ethyl acetate is formed by the reaction of ethanol and acetic acid and the equilibrium is represented as :
`CH_(3) COOH(l) +C_(2)H_(5)OH(l)hArr CH_(3)COOC_(2)H_(5)(l) +H_(2)O(l)`
(i) Write the concentration ratio (concentration quotient) Q for this reaction. Note that water is not in excess and is not a solvent in this reaction.
(ii) At 293 K, if one starts with 1.000 mol of acetic acid 0.180 mol of ethanol, there is 0.171 mol of ethyl acetate in the final equilibrium mixture . Calculate the equilibrium constant.
(iii) Starting with 0.50 mol of ethanol and 1.000 mol of acetic acid and maintaining it at 293 K, 0.214 mol of ethyl acetate is found after some time. Has equilibrium been reached?

Answer

(i) `[CH_(3)COOC_(2)H_(5)][H_(2)O]//[CH_(2)COOH][C_(2)H_(5)OH]`
(ii) `3.92` , (iii) value of `Q_(c)` is less than `K_(c)` therefore equilibrium is not attained.

Explanation

(i) Reaction quotient, `Q_(c) = ([CH_(3)COOC_(2)H_(5)][H_(2)O])/([CH_(3)COOH][C_(2)H_(5)OH])`
(ii) Let the volume of the reaction mixture be V. Also, here we will consider that water is a solvent and is present in excess.
The given reaction is :
`{:(,CH_(3)COOH_((l)),+,C_(2)H_(5)OH_((l)),harr,CH_(3)COOC_(2)H_(5(l)),,H_(2)O_((l))),("Initial conc.",1/(V)M,,(0.18)/(V)M,,0,,0),("At equilibrium",(1-0.171)/(V),,(0.18-0.171)/(V),,(0.171)/(V)M,,(0.171)/(V)M),(,=(0.829)/(V)M,,=(0.009)/(V) M,,,,):}`
Therefore, equilibrium costant for the given reaction is :
`K_(c) = ([CH_(3)COOC_(2)H_(5)][H_(2)O])/([CH_(3)COOH][C_(2)H_(5)OH])`
`= ((0.171)/(V)xx (0.171)/(v))/((0.829)/(V) xx (0.009)/(V)) = 3.919`
`= 3.92` (approximately)
(iii)Let the volume of the reaction mixture be V.
`{:(,CH_(3)COOH_((l)),+,C_(2)H_(5)OH_((l)),harr,CH_(3)COOC_(2)H_(5(l)),+,H_(2)O_((l))),("Initial conc.",(1.0)/(V)M,,(0.5)/(V)M,,0,,0),("After some time",(10-0.214)/(V),,(0.5-0.214)/(V),,(0.214)/(V)M,,(0.214)/(V)M),(,=(0.786)/(V)M,,=(0.286)/(V)M,,,,):}`
Therefore, the reaction quotient is,
`Q_(c) = ([CH_(3)COOC_(2)H_(5)][H_(2)O])/([CH_(3)COOH][C_(2)H_(5)OH])`
`= ((0.214)/(V)xx (0.214)/(V))/((0.786)/(V) xx (0.286)/(V))`
`= 0.2037`
`= 0204` (approximately)
Since `Q_(c) lt K_(c)` equilibrium has not been reached.