For the following equilibrium
showing the hydrolysis of an ester, find the correct equation for 𝐾 𝑐. CH3COOCH3 plus H2O is in
equilibrium with CH3COOH plus CH3OH.
In this question, we need to
determine the 𝐾 𝑐 for the hydrolysis of the ester methyl acetate, which produces
acetic acid and methanol when reacted with water. 𝐾 𝑐 is the equilibrium constant
for concentration. The equilibrium constant for
concentration expresses a value related to the ratio between the concentrations of
the reactants and products at equilibrium.
Let’s consider a generic
equilibrium reaction equation. In this equation, the lowercase
letters represent stoichiometric coefficients and the uppercase letters represent
chemical formulas. For the generic reaction equation,
we can write the following equation for the equilibrium constant for
concentration. 𝐾 𝑐 equals the concentration of
the products raised to their stoichiometric coefficients divided by the
concentration of the reactants raised to their stoichiometric coefficients.
It’s worth noting that species in
the solid phase and pure water when used as a solvent do not appear in the
equilibrium constant for concentration equation. All of the species involved in the
given reaction are liquids. In addition, water in this reaction
is a reactant, not just a solvent. So all of the species involved in
the reaction should appear in the equilibrium constant for concentration
With this in mind, we can follow
the generic equation to write the correct equation for 𝐾 𝑐 for this reaction. We find that to determine the
equilibrium constant for concentration for this reaction, we need to multiply the
concentration of acetic acid by the concentration of methanol then divide by the
concentration of methyl acetate and the concentration of water.
In conclusion, the correct equation
for 𝐾 𝑐 is 𝐾 𝑐 equals the concentration of CH3COOH times the concentration of
CH3OH divided by the concentration of CH3COOCH3 times the concentration of H2O.