100 mL of 0.06 M TRIS hydrochloride (C4H11NO3· HCl) is titrated with 1.0 M sodium hydroxide (NaOH). What is the pKa?
To determine the pKa of TRIS hydrochloride (C4H11NO3· HCl), we need to find the equivalence point of the titration. The reaction between TRIS hydrochloride and sodium hydroxide can be represented as follows:
C4H11NO3· HCl + NaOH → C4H11NO3 + NaCl + H2O
From the balanced equation, we can see that the mole ratio between TRIS and NaOH is 1:1. Therefore, the moles of TRIS hydrochloride in the solution are equal to the moles of NaOH used in the titration.
Given that the volume of TRIS hydrochloride solution is 100 mL and the concentration is 0.06 M, we can calculate the number of moles of TRIS hydrochloride:
moles of TRIS hydrochloride = volume (L) x concentration (mol/L)
moles of TRIS hydrochloride = 0.1 L x 0.06 mol/L
moles of TRIS hydrochloride = 0.006 mol
Since the mole ratio between TRIS and NaOH is 1:1, the number of moles of NaOH used in the titration is also 0.006 mol.
Now we can calculate the volume of 1.0 M NaOH solution required to reach the equivalence point:
volume of NaOH (L) = moles of NaOH / concentration (mol/L)
volume of NaOH = 0.006 mol / 1.0 mol/L
volume of NaOH = 0.006 L = 6 mL
At the equivalence point, the acidic proton of TRIS hydrochloride is neutralized by the sodium hydroxide, forming the conjugate base of TRIS. The pH at the equivalence point can be calculated using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Since we are at the equivalence point, the concentration of TRIS hydrochloride remaining is 0. To calculate the concentration of the conjugate base, [A-], we need to determine the concentration of TRIS as a weak base:
TRIS (C4H11NO3) consists of TRIS hydrochloride (C4H11NO3· HCl) and the monoprotic TRIS base (C4H12NO3).
moles of TRIS = moles of TRIS hydrochloride
moles of TRIS = 0.006 mol
Concentration of TRIS (weak base) = moles of TRIS / volume (L)
Concentration of TRIS = 0.006 mol / 0.1 L
Concentration of TRIS = 0.06 M
Since the concentration of the conjugate base [A-] is equal to the concentration of TRIS, we can substitute the values into the Henderson-Hasselbalch equation:
pH = pKa + log([0.06M]/[0])
pH = pKa + log(∞)
At the equivalence point, the concentration of the conjugate base is extremely high, so log(∞) can be considered as infinity. In this case, the pH is equal to the pKa. Therefore, the pKa of TRIS hydrochloride is unknown based on the information provided.
To find the pKa of TRIS hydrochloride (C4H11NO3· HCl), we need to determine the point of equivalence in the titration curve, which occurs when the number of moles of hydroxide ions (OH-) added equals the number of moles of acidic protons (H+) in TRIS hydrochloride.
In this reaction, TRIS hydrochloride acts as a weak acid, donating protons (H+) to hydroxide ions (OH-) from sodium hydroxide (NaOH). The balanced chemical equation for the reaction is:
C4H11NO3· HCl + OH- -> C4H11NO3 + H2O + Cl-
Given:
- Volume of TRIS hydrochloride solution (V1) = 100 mL = 0.100 L
- Concentration of TRIS hydrochloride (C1) = 0.06 M
- Concentration of sodium hydroxide (NaOH) (C2) = 1.0 M
First, we need to calculate the number of moles of TRIS hydrochloride present in the solution:
moles of TRIS hydrochloride (n1) = Concentration (C1) x Volume (V1)
= 0.06 M x 0.100 L
= 0.006 moles
Since TRIS hydrochloride donates only one proton (H+), the number of moles of hydroxide ions (OH-) required to reach the point of equivalence is also 0.006 moles.
Next, we can calculate the volume of sodium hydroxide solution (V2) required to react with the TRIS hydrochloride:
moles of NaOH (n2) = moles of TRIS hydrochloride (n1)
Volume of NaOH (V2) x Concentration of NaOH (C2) = n2
V2 = n2 / C2 = 0.006 moles / 1.0 M = 0.006 L = 6 mL
Therefore, the point of equivalence is reached when approximately 6 mL of 1.0 M sodium hydroxide solution is added to 100 mL of 0.06 M TRIS hydrochloride.
To determine the pKa, we need to know the equilibrium constant (Ka) for the reaction. Unfortunately, it is not provided. Without that information, it is not possible to calculate the pKa. The pKa value for TRIS hydrochloride might be available in reference sources or experimental data.