Question
Physical Chemistry
The equilibrium constant for the esterification of ethanol and acetic acid in an aqueous solution CH3COOH(aq) + C2H5OH(aq) CH3COOC2H5(aq) + H20(1) amounts to 0.566 at 298 K. The reaction mixture initially contains 0.04 mol dm-3 of acctic acid and 0.025 mol dm-3 of ethanol. Find the molar concentration of ethyl acetate at the equilibrium. Assume that the pH is low enough that CH3COOH is not dissociated at all and that the activity of water equals 1 just like for pure liquid water (after all, the solution is quite dilute). Hint: This problem requires you to keep an extra large number of significant digits in all intermediate calculations: otherwise, your final answer will be very inaccurate. Do not forget to check your answer in the end.
Explanation / Answer
K = [CH3COOC2H5]/[CH3COOH][C2H5OH]
at equilibrium [CH3COOH] = ( 0.04-x) moldm-3 , [C2H5OH] =(0.025-x)mol dm-3,
[CH3COOC2H5] = x ,
K = 0.566 = ( x)/(0.04-x)(0.025-x)
0.566 x^2 -1.03679x +0.000566 = 0
x = 0.000546 mol/dm3 = molar conc of ethyl acetate