A solution prepared by mixing 51.4 mL of 0.340 M AgNO3 and 51.4 mL of 0.340 M TlNO3 was titrated with 0.680 M NaBr in a cell containing a silver indicator electrode and a reference electrode of constant potential 0.175 V. The reference electrode is attached to the positive terminal of the potentiometer, and the silver electrode is attached to the negative terminal. The solubility constant of TlBr is Ksp = 3.6 × 10–6 and the solubility constant of AgBr is Ksp = 5.0 × 10–13.
I know how to do a regular titration with Ag. I am thrown off by the NaBr. How does that fit in with the calculations?
What is the cell voltage when the following volumes of 0.680 M NaBr have been added? (b) 1.0 mL (c) 13.2 mL (d) 24.7 mL (e) 25.6 mL (f) 26.0 mL (g) 38.9 mL (h) 51.4 mL (i) 52.0 mL
In this titration, the NaBr is used as a titrant to react with the silver ions (Ag+) and thallium ions (Tl+) in the given solution. The reaction between NaBr and Ag+ forms AgBr, and the reaction between NaBr and Tl+ forms TlBr. The presence of NaBr affects the solubility of AgBr and TlBr, leading to the formation of precipitates.
To understand how NaBr fits into the calculations, we need to consider the reaction equations and the solubility products (Ksp) of AgBr and TlBr.
1. Reaction equation for Ag+ with NaBr:
Ag+ (aq) + Br- (aq) → AgBr (s)
2. Reaction equation for Tl+ with NaBr:
Tl+ (aq) + Br- (aq) → TlBr (s)
The solubility product (Ksp) expressions for AgBr and TlBr are:
Ksp(AgBr) = [Ag+] [Br-]
Ksp(TlBr) = [Tl+] [Br-]
During the titration, the silver indicator electrode and the reference electrode are used to measure the potential difference (voltage) between them, which can be related to the concentration of the Ag+ ions in solution.
Now, let's break down the calculations step by step:
1. Calculate the amount of moles of Ag+ and Tl+ in the initial solution:
moles Ag+ = volume AgNO3 (L) × concentration AgNO3 (M)
moles Tl+ = volume TlNO3 (L) × concentration TlNO3 (M)
2. Determine the initial concentration of Ag+ and Tl+ in the mixed solution:
Ag+ (initial) = moles Ag+ / total volume of mixed solution (L)
Tl+ (initial) = moles Tl+ / total volume of mixed solution (L)
3. Calculate the formation of AgBr and TlBr based on the reactions with NaBr:
Using stoichiometry, you can determine the moles of AgBr and TlBr formed from the reaction with NaBr.
4. Calculate the resulting concentration of Ag+ and Tl+ after the reaction with NaBr:
Ag+ (final) = Ag+ (initial) - moles Ag+ reacted to form AgBr
Tl+ (final) = Tl+ (initial) - moles Tl+ reacted to form TlBr
5. Calculate the concentration of Br- ions formed from the reaction with NaBr:
The moles of Br- ions formed are equal to the moles of AgBr and TlBr formed.
6. Calculate the solubility of AgBr and TlBr using their respective Ksp values:
AgBr solubility = [Ag+] [Br-]
TlBr solubility = [Tl+] [Br-]
Keep in mind that the Ksp expression depends on the concentration of Ag+ and Tl+ at equilibrium, which are based on the reactions with NaBr. Therefore, calculating the concentrations and solubilities involves considering the reactions and the stoichiometry.
By following these steps, you can account for the presence of NaBr in the calculations and determine the resulting concentrations and solubilities of AgBr and TlBr in the solution.