Glutamate (Glu–) is the conjugate base form of glutamic acid (HGlu). The Ka of glutamic acid is 5.012 x 10^–5. You titrate 50 mL of 0.10 M sodium glutamate solution with 0.05 M HCl solution. Calculate the pH of the solution at the equivalence point.
Ive been trying to figure this out for hours! Please help me set this up!! thank you so much!!
You have 50 x 0.1 = 5 millimoles NaGlu which will require 100 mL of the 0.05M HCl. (HGlU) = 5 mmols/150 mL = 0.0333
.........HGlu ==> H^+ + Glu^-
I......0.0333.....0......0
C........-x........x......x
E......0.0333-x....x......x
Ka = (H^+)(Glu^-)/(HGlu)
Substitute from the ICE chart and solve for H^+, convert to pH.
........Glu^- + HOH ==> HGlu + OH^-
initial.
To calculate the pH of the solution at the equivalence point, we need to determine the concentration of the conjugate base, Glutamate (Glu–), at the equivalence point.
Let's start by calculating the number of moles of HCl that react with the Glutamate solution. The balanced chemical equation for the reaction between HCl and Glutamate is as follows:
HCl + Glu– -> GluH + Cl–
According to the equation, the stoichiometry is 1:1. This means that one mole of HCl reacts with one mole of Glutamate. Therefore, the number of moles of HCl can be calculated as follows:
moles of HCl = concentration of HCl × volume of HCl solution
moles of HCl = 0.05 M × V (where V is the volume of HCl solution added at the equivalence point)
Since the volume of HCl required to reach the equivalence point is not given, we can assume that it is the same as the volume of Glutamate solution used, which is 50 mL or 0.05 L.
moles of HCl = 0.05 M × 0.05 L = 0.0025 moles
Since the stoichiometric ratio is 1:1, this means that 0.0025 moles of Glutamate also reacted.
Now, let's calculate the concentration of Glutamate (Glu–) in the solution at the equivalence point. Initially, we had 0.10 M Glutamate, and 0.0025 moles reacted:
moles of Glutamate = initial moles of Glutamate – moles of Glutamate reacted
moles of Glutamate = 0.10 M × 0.05 L – 0.0025 moles
moles of Glutamate = 0.005 moles
Next, let's calculate the concentration of Glutamate at the equivalence point:
concentration of Glutamate = moles of Glutamate / volume of Glutamate solution
concentration of Glutamate = 0.005 moles / 0.05 L
concentration of Glutamate = 0.10 M
Now that we have the concentration of Glutamate at the equivalence point, we can calculate the pOH using the Ka value of Glutamic acid:
Ka = [H+][Glu–] / [HGlu]
Since Glutamic acid and Glutamate are in a 1:1 ratio, [HGlu] is equal to the initial concentration of Glutamic acid, which is 0.10 M.
Using the equation, the concentration of H+ can be calculated:
[H+] = (Ka × [HGlu]) / [Glu–]
[H+] = (5.012 x 10^–5) × (0.10 M) / (0.10 M)
[H+] = 5.012 x 10^–5 M
Now, we can calculate the pOH:
pOH = -log10([OH–]) = -log10(Kw / [H+])
pOH = -log10(1.0 x 10^–14 / 5.012 x 10^–5)
pOH ≈ 7.30
Since pH + pOH = 14 at 25°C, the pH at the equivalence point is:
pH = 14 - pOH
pH = 14 - 7.30
pH ≈ 6.70
Therefore, the pH of the solution at the equivalence point is approximately 6.70.
To solve this problem, we need to understand the concept of equivalence point and use it to calculate the pH at that point.
The equivalence point is the point in a titration where the moles of acid added is equal to the moles of base present (or vice versa). At this point, the solution contains a mixture of the conjugate base and its conjugate acid in equal amounts, resulting in a buffer solution.
Given:
- Volume of sodium glutamate solution (V1) = 50 mL = 0.050 L
- Concentration of sodium glutamate (C1) = 0.10 M
- Concentration of HCl solution (C2) = 0.05 M
First, we need to determine the moles of sodium glutamate (moles of base) and moles of HCl (moles of acid) in the solution.
Moles of sodium glutamate (n1) = C1 * V1
moles of sodium glutamate (n1) = 0.10 M * 0.050 L = 0.005 moles
Since HCl is a strong acid, it will completely dissociate in water, meaning that the moles of HCl will be equal to the moles of H+ formed. Therefore, the moles of HCl is also 0.005 moles.
At the equivalence point, the moles of acid (H+) will react with the moles of the base (conjugate base of Glu-) to form water. This means that there will be no excess moles of either the acid or base remaining in solution.
Therefore, we now have 0.005 moles of the conjugate base (Glu-) and 0.005 moles of the conjugate acid (H+).
Now, let's calculate the concentrations of the conjugate base (Cbase) and the conjugate acid (Cacid).
Cbase = nbase / V1
Cbase = 0.005 moles / 0.050 L
Cbase = 0.10 M
Cacid = nacid / V1
Cacid = 0.005 moles / 0.050 L
Cacid = 0.10 M
Since we have equal concentrations of the conjugate base and conjugate acid and they are in a 1:1 ratio, the pH at the equivalence point can be calculated using the Henderson-Hasselbalch equation:
pH = pKa + log (Cbase / Cacid)
The pKa for glutamic acid is given as 5.012 x 10^–5.
Now, plug in the values:
pH = -log(5.012 x 10^–5) + log(0.10 / 0.10)
pH = -log(5.012 x 10^–5) + log(1)
pH = -(-4.30) + 0
pH = 4.30
Therefore, the pH of the solution at the equivalence point is 4.30.