Vanadium is an environmental pollutant originating from some types of steel, but

also from the combustion of fossil fuels. The amount of V2+ in an unknown sample is
determined by potentiometric titration by 7.62 mM permanganate ion, MnO4
-
. 25.00 mL of
unknown was titrated with 12.38 mL of 7.62 mM MnO4
- using a SCE reference electrode (Eref =
0.241 V). pH of the solution was maintained at pH = 4.00. Determine the potential at the
equivalence point and the concentration of vanadium in the unknown sample.
V3+ + e- → V2+ Eo = -0.255 V
MnO4
- + 8H+ + 5e- → Mn2+ + 4 H2O Eo = +1.507 V

To determine the potential at the equivalence point and the concentration of vanadium in the unknown sample, we need to follow these steps:

Step 1: Write the balanced equation for the redox reaction between V2+ and MnO4-:
V2+ + MnO4- + H+ → V3+ + Mn2+ + H2O

Step 2: Calculate the number of moles of MnO4- used in the titration:
Volume of MnO4- = 12.38 mL
Concentration of MnO4- = 7.62 mM = 7.62 × 10^-3 M

Number of moles of MnO4- = (Volume × Concentration of MnO4-) / 1000
= (12.38 × 7.62 × 10^-3) / 1000

Step 3: Determine the number of electrons transferred in the redox reaction:
From the balanced equation, we can see that 5 electrons are transferred for every mole of MnO4-.

Number of electrons transferred = 5 × (Number of moles of MnO4-)

Step 4: Calculate the number of moles of V2+ in the unknown sample:
From the balanced equation, we know that 1 mole of V2+ reacts with 1 mole of MnO4-.

Number of moles of V2+ = Number of moles of MnO4-

Step 5: Determine the charge associated with the redox reaction:
V3+ + e- → V2+ Eo = -0.255 V

The charge associated with the redox reaction = -1

Step 6: Calculate the potential at the equivalence point:
Potential at the equivalence point = Eo - (0.05916 / n) × log([V2+]/[V3+])
where n is the number of electrons transferred and [V2+] and [V3+] are the concentrations of V2+ and V3+.

Substitute the values:
Potential at the equivalence point = -0.255 - (0.05916 / 5) × log([V2+]/[V3+])

Step 7: Calculate the concentration of vanadium in the unknown sample:
Substitute the values from Step 2, Step 3, and Step 4 into the equation:

Potential at the equivalence point = -0.255 - (0.05916 / 5) × log(Number of moles of V2+ / Number of moles of MnO4-)

Solve the equation to obtain the potential at the equivalence point and the concentration of vanadium in the unknown sample.