Complete hydrolysis of 25 mM ethyl acetate in an enzyme 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 pH at the end of the reaction, we need to consider the ionization of Tris (hydroxymethyl) aminomethane and acetic acid.
First, let's calculate the concentration of Tris and acetic acid after the hydrolysis reaction.
We are given:
Initial concentration of ethyl acetate = 25 mM
NaCl concentration = 40 mM
Tris-Cl concentration = 0.2 M
Since ethyl acetate hydrolysis produces acetic acid, we need to take into account the change in concentration for the acetic acid.
The reaction equation for hydrolysis of ethyl acetate is:
Ethyl acetate + H2O -> Acetic acid + Ethanol
Since 1 mole of ethyl acetate produces 1 mole of acetic acid, the concentration of acetic acid after hydrolysis will be the same as the initial concentration of ethyl acetate, which is 25 mM.
Next, let's calculate the concentration of Tris and acetic acid after the reaction:
Concentration of Tris = 0.2 M
Concentration of acetic acid = 25 mM
To determine the pH at the end of the reaction, we need to consider the ionization of Tris and acetic acid.
Tris is a weak base and can accept a proton (H+). Acetic acid is a weak acid and can donate a proton (H+).
The pKa values given for Tris and acetic acid are:
pKa Tris = 8.1
pKa acetic acid = 4.76
To calculate the pH, we need to determine the ratio of the concentration of Tris base to its conjugate acid (Tris+).
pKa = -log10(Ka)
For Tris, we can use the following equation:
Ka = [Tris+][H+]/[Tris]
Ka is the acid dissociation constant and is given by:
Ka = 10^(-pKa)
From this equation, we can calculate the concentrations of Tris+ and Tris.
Tris+ concentration = [H+][Tris]/Ka
Tris concentration = [Tris+]/[H+]
Using the given pKa value and the concentration of Tris, we can determine the concentrations of Tris+ and Tris.
Similarly, we can do the same calculations for acetic acid and its conjugate base (acetate ion).
After determining the concentrations of Tris+ and acetic acid, we can then use the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa + log10([conjugate base]/[acid])
Substitute the values we obtained into the Henderson-Hasselbalch equation to calculate the pH at the end of the reaction.
To determine the pH at the end of the reaction, we need to consider the dissociation of Tris buffer and the formation of acetic acid during the hydrolysis of ethyl acetate.
Step 1: Dissociation of Tris buffer
Tris buffer dissociates according to the following equation:
Tris-H + H2O ⇌ Tris- + H3O+
The initial concentration of Tris-Cl is 0.2 M.
At equilibrium, the concentration of Tris-H will be equal to the concentration of Tris-. Let's denote it as x M.
Hence, [Tris-] = [Tris-H] = x M
[H3O+] = x M
Step 2: Formation of acetic acid
Ethyl acetate is hydrolyzed to form acetic acid and ethanol:
C2H5OOCCH3 + H2O ⇌ CH3COOH + C2H5OH
The initial concentration of ethyl acetate is 25 mM, and its hydrolysis will produce an equal amount of acetic acid.
[H3O+] = [CH3COOH] in mM
Step 3: Equilibrium expression for acetic acid
The dissociation of acetic acid can be described by the following equation:
CH3COOH + H2O ⇌ CH3COO- + H3O+
The equilibrium constant expression is:
Ka = [CH3COO-][H3O+]/[CH3COOH]
The pKa of acetic acid is 4.76, so we can calculate the Ka using the formula:
Ka = 10^(-pKa)
Step 4: Applying the law of mass action
At equilibrium, the concentrations of reactants and products are:
[CH3COO-] = x M
[H3O+] = x M
[CH3COOH] = 25 mM - x M
Now, we can substitute these values into the equilibrium constant expression:
Ka = x * x / (25 mM - x M)
Step 5: Calculate the value of x
Since the Ka is very small compared to the initial concentration of ethyl acetate (25 mM), we can assume that the amount of ethyl acetate that hydrolyzes is much greater than the amount of acetic acid formed.
Hence, x ≈ 25 mM
Step 6: Calculate the pH at the end of the reaction
At the end of the reaction, the concentration of [H3O+] is equal to the concentration of acetic acid:
[H3O+] = [CH3COOH] = 25 mM - x ≈ 0 mM
Finally, we can calculate the pH using the formula:
pH = -log10[H3O+]
pH = -log10[0 mM]
pH = -log10(0)
As the concentration of [H3O+] is zero,
pH = -log10(0) is undefined
Therefore, the pH at the end of the reaction is undefined or not applicable.