Analytical Chemistry Titration(s)

Question

The potential is measured using a Pt indicator electrode (red (+) lead) and a Ag/AgCl reference electrode (black (-) lead) as 50.0 mL of 0.10 M Tl+ is titrated with 0.20 M Co3+ . Predict the measured potential (a) at the half-equivalence point, (b) somewhere before the equivalence point (c) at the equivalence point and (d) somewhere past the equivalence point.

Tl3+ + 2e¯ ⇋ Tl+ Eo = 1.28 V

Co3+ + e¯ ⇋ Co2+ Eo = 1.92 V

Steps on how to solve a question like this?

Answer 1

To predict the measured potential at different stages of the titration, we need to use the Nernst equation. The reaction you're considering involves the titration of Tl++ with Co3+3+, and we'll calculate the potential at various points in the titration process.

Given:

1. Tl3++2e−↔3++2e−↔ Tl++; E∘=1.28 VE∘=1.28 V
2. Co3++e−↔3++e−↔ Co2+2+; E∘=1.92 VE∘=1.92 V

Titration Details:

1. 50.0 mL of 0.10 M Tl++
2. 0.20 M Co3+3+

Reaction in Titration: Tl++Co3+→Tl3++Co2+Tl++Co3+→Tl3++Co2+

1. At the Half-Equivalence Point

At the half-equivalence point, the amount of Co3+3+ added is half the amount required to completely react with Tl++.

Half-Equivalence Point Calculations:

1. Determine Moles of Tl++: Moles of Tl+=0.10 M×0.050 L=0.005 molesMoles of Tl+=0.10 M×0.050 L=0.005 moles
2. Moles of Co3+3+ Required at Equivalence Point: Since it takes 1 mole of Co3+3+ to react with 1 mole of Tl++, you need 0.005 moles of Co3+3+ to reach equivalence.
3. Moles of Co3+3+ Added at Half-Equivalence Point: Moles of Co3+=0.005/2=0.0025 molesMoles of Co3+=0.005/2=0.0025 moles
4. Concentration of Co3+3+ at Half-Equivalence Point: The volume of Co3+3+ solution added is:Volume=MolesConcentration=0.00250.20=0.0125 L=12.5 mLVolume=ConcentrationMoles​=0.200.0025​=0.0125 L=12.5 mL
5. Concentration of Tl++ and Co3+3+ at Half-Equivalence Point:
6. Tl++ is still in solution with concentration = 0.005 moles / 0.0625 L = 0.08 M
7. Co3+3+ is equal to its initial concentration due to the equal volumes.
8. Calculate Potential:
9. The cell potential can be calculated using the Nernst equation for the cell reaction: Tl++Co3+→Tl3++Co2+Tl++Co3+→Tl3++Co2+
10. Nernst Equation for the Cell Reaction: E=E∘−RTnFln⁡([Products][Reactants])E=E∘−nFRT​ln([Reactants][Products]​)
11. E=E∘−RTnFln⁡([Co2+][Tl3+][Tl+][Co3+])E=E∘−nFRT​ln([Tl+][Co3+][Co2+][Tl3+]​)
12. E=(1.92−1.28)−0.0591nlog⁡(0.08⋅0.10.1⋅0.08)E=(1.92−1.28)−n0.0591​log(0.1⋅0.080.08⋅0.1​)
13. E = 0.64 V (simplified calculation for conceptual understanding)

2. Before the Equivalence Point

Example Calculation:

1. Concentration of Tl++ and Co3+3+:
2. Let’s assume we have added 10 mL of Co3+3+, so: Moles of Co3+=0.20 M×0.010 L=0.002 molesMoles of Co3+=0.20 M×0.010 L=0.002 moles
3. The remaining Tl++: Concentration of Tl+=0.005 moles0.060 L=0.083 MConcentration of Tl+=0.060 L0.005 moles​=0.083 M
4. The concentration of Co3+3+: Concentration of Co3+=0.002 moles0.060 L=0.033 MConcentration of Co3+=0.060 L0.002 moles​=0.033 M
5. Nernst Equation:
6. E=1.92−0.05911log⁡(0.0830.033)E=1.92−10.0591​log(0.0330.083​) E≈1.89 VE≈1.89 V

3. At the Equivalence Point

At the equivalence point, the amount of Co3+3+ added is exactly sufficient to react with all Tl++.

Concentrations:

1. All Tl++ has been converted to Tl3+3+, and all Co3+3+ has been converted to Co2+2+.

Nernst Equation:

E=E∘ (where the cell reaction is essentially complete) E=E∘ (where the cell reaction is essentially complete) 

E=1.92−1.28 V=0.64 VE=1.92−1.28 V=0.64 V

4. Past the Equivalence Point

After equivalence, excess Co3+3+ will be present.

Example Calculation:

1. Excess Co3+3+:
2. Let’s assume we have added 60 mL of Co3+3+, so: Moles of Co3+=0.20 M×0.060 L=0.012 molesMoles of Co3+=0.20 M×0.060 L=0.012 moles
3. There will be excess Co3+3+: Concentration of Co3+=0.012 moles0.060 L=0.20 MConcentration of Co3+=0.060 L0.012 moles​=0.20 M
4. Nernst Equation:
5. E=1.92−0.05911log⁡(0.0830.20)E=1.92−10.0591​log(0.200.083​) E≈1.95 VE≈1.95 V

In summary:

1. Half-Equivalence Point Potential: ~0.64 V
2. Before Equivalence Point: ~1.89 V (Example with 10 mL Co3+3+)
3. At Equivalence Point: ~0.64 V
4. Past Equivalence Point: ~1.95 V (Example with 60 mL Co3+3+)