Complete hydrolysis of 25 mM ethyl acetate in an enzyme (i.e., esterase)-catalyzed reaction is carried out in a 40 mM NaCl solution buffered by 0.2 M Tris-Cl, pH 9.1. What is the pH at the end of the reaction? (For Tris base, which is the abbreviation for Tris (hydroxymethyl) aminomethane, pKa = 8.1; for acetic acid, pKa = 4.76)
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To determine the final pH of the reaction, we need to consider the dissociation of the Tris buffer and the acetic acid formed during the hydrolysis of ethyl acetate.
Step 1: Write the balanced equation for the hydrolysis reaction of ethyl acetate:
Ethyl acetate + H2O ⇌ Ethanol + Acetic acid
Step 2: Determine the concentration of acetic acid (CH3COOH) produced at the start:
Given that the initial concentration of ethyl acetate is 25 mM, and assuming complete hydrolysis, the concentration of acetic acid formed is also 25 mM.
Step 3: Calculate the ratio of dissociated to undissociated acetic acid:
By using the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
Given that the pKa of acetic acid is 4.76, we can substitute the values:
4.76 = 4.76 + log([A-]/[HA])
The concentration of undissociated acetic acid ([HA]) is equal to the initial concentration (25 mM), and the concentration of dissociated acetic acid ([A-]) is unknown. Rearranging the equation yields:
log([A-]/25) = 0
Therefore, [A-] = 25 mM, indicating that acetic acid is completely dissociated.
Step 4: Determine the concentration of Tris (Tris (hydroxymethyl) aminomethane) buffer:
Given that the buffer solution is 0.2 M Tris-Cl, the concentration of Tris is 0.2 M.
Step 5: Calculate the pH shift caused by Tris and acetic acid:
Because Tris is a weak base, it will primarily exist in the protonated form (BH+) at pH values below its pKa. However, at pH values above the pKa, it will mainly exist in the deprotonated form (B).
Considering the pKa of Tris as 8.1 and its concentration as 0.2 M, we can calculate the ratio of dissociated to undissociated Tris using the Henderson-Hasselbalch equation:
pH = pKa + log ([B]/[BH+])
pH = 8.1 + log ([B]/[0.2])
To find the concentration of B, we need to determine the concentration of BH+:
BH+ + OH- ⇌ B + H2O
Since both NaCl and Tris dissociate into Na+ and Cl- ions, the OH- concentration is determined by the dissociation of water:
[H2O] = [H+] x [OH-]
Since water is neutral, [H+] = [OH-] = 10^-7 M
Substituting into the equation:
[H2O] = 10^-14/10^-7
[H2O] = 10^-7 M
Since Tris is a weak base, the concentration of BH+ formed will be negligible compared to the initial Tris concentration. Therefore, we can assume that the concentration of B is approximately equal to the initial Tris concentration of 0.2 M.
Substituting into the Henderson-Hasselbalch equation:
pH = 8.1 + log(0.2/0.2)
pH = 8.1
Therefore, the pH at the end of the reaction is pH = 8.1.
Note: In this calculation, we have assumed that the reaction does not significantly affect the concentration of Tris, NaCl, or water. Additionally, we have assumed that the reaction is well-buffered and proceeds to completion, ensuring negligible changes in pH due to the hydrolysis reaction.