Library / Solution chemistry, equilibria and kinetics / SCH-25
Solution chemistry, equilibria and kinetics
Free silver in a chloride precipitation titration
Free silver concentration while AgCl solid is present, from d, the analytical silver minus analytical chloride concentration after dilution, and Ksp.
- Ref
- SCH-25
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- [Ag⁺] [mol/L]
During the titration of chloride with silver nitrate, with solid AgCl present, [Ag⁺][Cl⁻] = Ksp and the mass balance gives [Ag⁺] − [Cl⁻] = d, where d is the analytical silver minus the analytical chloride (after dilution). Solving gives [Ag⁺] = ½(d + √(d² + 4Ksp)). When d is negative (chloride in excess) the equivalent form 2Ksp/(√(d² + 4Ksp) − d) avoids losing digits to cancellation.
Free silver concentration while AgCl solid is present, from d, the analytical silver minus analytical chloride concentration after dilution, and Ksp. For d below zero (excess chloride) a stable equivalent form is used. No other ligands or large activity effects.
Calculator
- Free chloride concentration, [Ag⁺] − d0.001 mol/L
- pAg, −log₁₀[Ag⁺]5
- Ion product, [Ag⁺][Cl⁻] (equals Ksp)1×10−8
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With 9.9×10−4 mol/L of excess chloride, the free silver is 1×10−5 mol/L, pAg 5.
- At the equivalence point (d = 0) it equals √Ksp = 1×10−4 mol/L, and pAg jumps by several units across that point.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol/L) | Local step | Change in result |
|---|---|---|---|---|---|---|
| d Analytical Ag minus analytical Cl | −0.01 to 0.01 mol/L | 9.999e-7 | 0.01 | 0.01 | +0.01 mol/L | +90,000 % |
| Ksp Solubility product (concentration basis) | 1e-12 to 1e-6 | 1.01e-9 | 6.208e-4 | 6.208e-4 | +10% | +9.89 % |
Sweep of Analytical Ag minus analytical Cl
| Analytical Ag minus analytical Cl (mol/L) | Free silver concentration (mol/L) |
|---|---|
| −0.01 | 9.999e-7 |
| −0.0075 | 1.333e-6 |
| −0.005 | 1.999e-6 |
| −0.0025 | 3.994e-6 |
| 0 | 1e-4 |
| 0.0025 | 0.002504 |
| 0.005 | 0.005002 |
| 0.0075 | 0.007501 |
| 0.01 | 0.01 |
Sweep one variable
Variables and how each one contributes
Free silver concentration
What the equation gives you. Everything else feeds it.
Analytical Ag minus analytical Cl
The analytical silver minus the analytical chloride concentration after dilution, in mol/L. A more positive d (more silver) raises the free silver, sharply as it passes zero. Raising it by 10 % (to −0.001089) moves the result by −8.93 %, from 1×10−5 to 9.107×10−6 mol/L.
Solubility product (concentration basis)
The solubility product of AgCl, concentration basis. A larger Ksp raises the free silver, most at the equivalence point (d = 0). Raising it by 10 % (to 1.1×10−8) moves the result by +9.89 %, from 1×10−5 to 1.099×10−5 mol/L.
Worked example with the values above
- Square-root term: √(d² + 4Ksp) = 0.00101 mol/L.
- With d < 0 use 2Ksp/(that − d) = 2×10−8 / 0.002.
- [Ag⁺] = 1×10−5 mol/L.
Assumptions and limits
- Complete, fast and well-defined reactions with a clear stoichiometry.
- Volumes in litres or in a single consistent unit, and calibrated glassware and electrodes.
Common mistakes
- Using the total silver in place of the difference d between silver and chloride.
- Ignoring dilution when calculating d.
- Ignoring complexation of silver by excess chloride at high concentrations.
Statistics and uncertainty
Burette readings are good to ±0.02 to 0.05 mL, so a 25 mL titre has a relative error near 0.1 to 0.2 %, and the endpoint-detection error adds to it.
Where it is used
- Analysing antacids, alkalinity, chloride and other titratable species.
- Estimating the endpoint error of a titration.
Maths you need
- Stoichiometry: mole ratios in a balanced equation
- Equivalence point: where the reagent amounts match exactly
- Titre: the volume of titrant delivered