The esterification equilibrium

Exercise 6

    

To synthesize ethyl butanoate (banana flavor), $1 \;mol$ of carboxylic acid reacts with $3\; mol$ of alcohol. 1) Establish the esterification reaction 2) Water is removed by a desiccant to the extent that the amount of water will be $0.2\;mol$ at equilibrium. Knowing that the equilibrium constant is $ 3.00$, calculate the yield of ester.

1) $CH_3CH_2CH_2COOH$ $+$ $HOCH_2CH_3$ $\leftrightarrows$ $CH_3CH_2CH_2COOCH_2CH_3$ 2) At equilibrium: $n_{ester}$ $=$ $x$ $n_{eau}$ $=$ $0.2$ $n_{acide}$ $=$ $1-x$ $n_{alcool}$ $=$ $3-x$ $K$ $=$ $\frac{n_{ester}\cdot n_{eau} }{n_{acide}\cdot n_{alcool}}$ $3.00$ $=$ $\frac{0,2x }{(1-x)(3-x)}$ $-3x^2$ $+$ $12.2x$ $-$ $9$ $=$ $0$ Only one reasonable solution: $x$ $=$ $0.968$ Yield= $\frac{n_{ester\; obtenu}}{n_{ester\; maximum}}$ = $0.968$