Question

An aqueous solution that $2.00\mathrm{M}$ in ${\mathrm{AgNO}}_3$ is slowly added from a buret to an aqueous solution that is $0.0100\mathrm{M}$ in ${\mathrm{Cl}}^{-}$ and $0.250\mathrm{M}$ in ${\mathrm{I}}^{-}$. (a) Which ion, ${\mathrm{Cl}}^{-}$ or ${\mathrm{I}}^{-}$, is the first to precipitate? (b) When the second ion begins to precipitate, what is the remaining concentration of the first ion? (c) Is the separation of ${\mathrm{Cl}}^{-}$ and ${\mathrm{I}}^{-}$ feasible by fractional precipitation in this solution?

Short answer

The iodide ions will precipitate first, before the chloride ions. When the iodide ions begin to precipitate, the remaining Cl- concentration will be 0.0100 M. And yes, the separation of Cl- and I- is feasible by fractional precipitation in this solution.

Step-by-step solution

Identify the Ksp values for AgCl and AgI

The Ksp values for AgCl and AgI are $1.8x{10}^{-10}$ and $8.3x{10}^{-17}$ respectively. The smaller Ksp value signifies the lower solubility, so AgI would be less soluble than AgCl.

Determine which ion will precipitate first

Because the Ksp of AgI is smaller than that of AgCl, iodide ions (I-) will form a precipitate with Ag+ ions before chloride ions (Cl-) do.

Calculate the remaining concentration of Cl- when I- begins to precipitate

The amount of Ag+ necessary to precipitate I- is equal to the initial I- concentration, 0.250 M. When that much AgNO3 has been added, all the I- has reacted, but none of the Ag+ has reacted with Cl-. Therefore, the Cl- concentration remains at its initial value of 0.0100 M.

Calculate whether the separation of Cl- and I- is feasible

The molar solubility of Cl- can be derived from Ksp (AgCl), considering no reaction has occurred with Ag+ yet. Using the equation $Ksp=[Ag+][Cl-]$, the required [Ag+] to begin precipitation of Cl- is: $[Ag+]=Ksp/[Cl-]=(1.8x{10}^{-10})/0.0100=1.8x{10}^{-8}M$. This is significantly less than the concentration of Ag+ necessary to precipitate I- (0.250 M), rendering separation by fractional precipitation feasible in this case, as AgI precipitates before any AgCl does.

Key concepts

Solubility Product Constant (Ksp)

Understanding the solubility of compounds is a key part of predicting the outcome of reactions in solution. In chemistry, the solubility product constant (Ksp) is a vital concept that helps us do just that. It quantifies the solubility of a sparingly soluble compound under a given set of conditions. The Ksp is the product of the concentrations of the ionic constituents of a compound, each raised to the power of its coefficient in the balanced equation.

For a generic salt AB that dissociates into A+ and B-, the Ksp expression would be written as: $$Ksp=[A^{+}][B^{-}]$$
Where $$A+$$ and $$B-$$ are the concentrations of the ions in moles per liter. The value of Ksp is set for a particular compound at a specific temperature, and it becomes a crucial factor in predicting whether a precipitate will form in a solution.

Ion Precipitation Order

When multiple ions are present in a solution, it's useful to know the order in which they will precipitate. This follows the rule that the ion with the lowest solubility (thus the smallest Ksp) will precipitate first. In a solution containing both chloride (Cl-) and iodide (I-) ions, for instance, we can compare their Ksp values when reacted with a common cation like silver (Ag+).

Determining Precipitation Sequence

For two silver salts, say AgCl and AgI, the respective Ksp values are key indicators. A smaller Ksp implies a salt is less soluble. Thus, AgI with its smaller Ksp compared to AgCl will precipitate out of solution first upon the addition of Ag+ ions. This is because it reaches its solubility limit more quickly than the salt with the higher Ksp.

Concentration Calculation

Calculating ion concentrations is critical when we wish to determine at what point a precipitate will form or to assess the feasibility of a separation process like fractional precipitation.

To find the concentration of ions left in solution after a reaction, we can use stoichiometry and the initial concentrations of the reactants. For the exercise given, when Ag+ is added to a mixture of Cl- and I-, we calculate the remaining Cl- concentration after all I- has precipitated by acknowledging that the AgI reaction has gone to completion. The concentration of Cl- remains unchanged since no AgCl has formed yet. This step is vital in understanding how much more Ag+ needs to be added to the solution to start precipitating the next ion.

Solubility and Ksp Relationship

The relationship between solubility and Ksp is reciprocal; as one increases, the other decreases. Knowing this helps in fractional precipitation, a technique used to separate ions based on their differing solubilities. The solubility of an ion in a solution can be calculated from its Ksp value if we have the concentration of the other ion present in the solution.

For example, if we want to separate Cl- from I- by precipitation, we add Ag+ slowly and utilize the difference in Ksp values. The lower the Ksp of the compound, the less soluble it is, resulting in its precipitation at a lower concentration of Ag+. With the known initial concentration of Cl- and its Ksp with Ag+, we can precisely calculate the threshold concentration of Ag+ needed to start precipitating Cl-, thus confirming whether fractional precipitation would successfully separate the two ions.