Find the approximate pH range suitable for the separation of Fe3+ and Zn2+ by precipitation of Fe(OH)3 from a solution that is initially 0.048 M in both Fe3+ and Zn2+.

To separate Fe3+ and Zn2+ by precipitation of Fe(OH)3, we need to find the pH range where Fe(OH)3 precipitates, but Zn(OH)2 stays soluble. We'll do this by examining their solubility products (Ksp) and calculating the pH range needed for precipitation.

The solubility product (Ksp) of Fe(OH)3 is 2.79 × 10^-39, and the solubility product of Zn(OH)2 is 3.0 × 10^-17.

For Fe(OH)3, the balanced equation and the corresponding solubility product expression is:
Fe³⁺ + 3OH⁻ ⇌ Fe(OH)₃(s), Ksp = [Fe³⁺][OH⁻]³

For Zn(OH)2, the balanced equation and the corresponding solubility product expression is:
Zn²⁺ + 2OH⁻ ⇌ Zn(OH)₂(s), Ksp = [Zn²⁺][OH⁻]²

Initially, the concentrations of Fe3+ and Zn2+ are both 0.048 M. Since we want Fe(OH)3 to precipitate, but not Zn(OH)2, we need to find the pH at which the concentrations of the ions in the solution exceed their solubility product limits.

For Fe(OH)3:
2.79 × 10^-39 = [(0.048)][OH⁻]³
[OH⁻]³ = 2.79 × 10^-39 / 0.048
[OH⁻]³ ≈ 5.81 × 10^-38
[OH⁻] ≈ 3.86 × 10^-13

To calculate the pH where Fe3+ begins to precipitate, we can use the relation:
pH = 14 - pOH
pOH = -log10[OH⁻]
pOH ≈ -log10(3.86 × 10^-13) ≈ 12.41
pH ≈ 14 - 12.41 ≈ 1.59

Now, we need to make sure that at this pH, Zn(OH)₂ will remain soluble. So we'll find the maximum concentration of OH⁻ that allows Zn(OH)₂ to be soluble:

For Zn(OH)2:
3.0 × 10^-17 = [(0.048)][OH⁻]²
[OH⁻]² = 3.0 × 10^-17 / 0.048
[OH⁻]² ≈ 6.25 × 10^-16
[OH⁻] ≈ 7.90 × 10^-8

Comparing the OH⁻ concentrations for both precipitates:
[OH⁻]Fe(OH)₃ ≈ 3.86 × 10^-13
[OH⁻]Zn(OH)₂ ≈ 7.90 × 10^-8

Since [OH⁻]Fe(OH)₃ is lower than [OH⁻]Zn(OH)₂, and the pH at which Fe(OH)3 begins to precipitate is 1.59, we can say that the separation of Fe3+ and Zn2+ by precipitation of Fe(OH)3 can occur at a pH of approximately 1.59, aslong as[^2] the pH remains below the point where Zn(OH)₂ starts to precipitate.

Refining this value further may require additional calculations and experimentation, but this approximate pH value should provide an initial estimate for the separation process.

To determine the approximate pH range suitable for the separation of Fe3+ and Zn2+ by precipitation of Fe(OH)3, we need to consider the solubility products of the hydroxides for both ions.

The solubility product constant (Ksp) for Fe(OH)3 can be written as:

Ksp = [Fe3+][OH-]^3

Similarly, the solubility product constant for Zn(OH)2 can be written as:

Ksp = [Zn2+][OH-]^2

Since both Fe3+ and Zn2+ are present in the initial solution, we need to find the pH range where Fe(OH)3 will precipitate while Zn(OH)2 remains soluble.

The pH at which Fe(OH)3 begins to precipitate can be found by considering the solubility of Fe(OH)3. At this pH, the concentration of hydroxide ions will exceed the solubility product of Fe(OH)3, causing precipitation.

We can calculate the concentration of hydroxide ions ([OH-]) using the given initial concentrations of Fe3+ and Zn2+.

Since Fe3+ and Zn2+ are both present in equal concentration, we can assume that the concentration of each is approximately half of the initial concentration:

[Fe3+] ≈ 0.048 M / 2 = 0.024 M
[Zn2+] ≈ 0.048 M / 2 = 0.024 M

Let's assume the concentration of OH- is x M.

Using the stoichiometry of the reaction Fe(OH)3 ⇌ Fe3+ + 3OH-, we can write the equation:

[Fe3+] = 3[OH-]

Plugging in the values:

0.024 M = 3x
x ≈ 0.008 M

So, the approximate concentration of OH- is 0.008 M.

Next, we can calculate the pOH:

pOH = -log([OH-]) = -log(0.008) ≈ 2.1

Finally, we can use the relationship between pH, pOH, and pKw (ion product of water) to find the pH:

pH + pOH = pKw

pH = pKw - pOH = 14 - 2.1 ≈ 11.9

Therefore, the approximate pH range suitable for the separation of Fe3+ and Zn2+ is between 11.9 and higher pH values where Fe(OH)3 starts to precipitate while Zn(OH)2 remains soluble.

To find the approximate pH range suitable for the separation of Fe3+ and Zn2+ by precipitation of Fe(OH)3, we need to consider their respective solubility products and their effect on the pH.

The solubility product (Ksp) of Fe(OH)3 is essential in understanding its solubility behavior. Fe(OH)3 can be expressed as:

Fe(OH)3(s) ⇌ Fe3+(aq) + 3OH-(aq)

The solubility product expression for Fe(OH)3 is:

Ksp = [Fe3+][OH-]^3

The Ksp of Fe(OH)3 is 10^-38.

When examining the presence of both Fe3+ and Zn2+ in solution, it is important to note that Zn(OH)2 is also an insoluble hydroxide that could precipitate. However, it has a much higher solubility product compared to Fe(OH)3 (Ksp ≈ 10^-16), suggesting that it will not precipitate under the conditions of this problem.

To determine the pH range suitable for the precipitation of Fe(OH)3, we need to consider the common ion effect. The common ion effect states that the solubility of a compound is reduced when a common ion is present in the solution.

In this case, the common ion is OH-. By adding OH- to the solution, the concentration of OH- ions will increase, shifting the equilibrium towards the formation of more Fe(OH)3 precipitates.

To find the pH range suitable for the separation, we need to determine the concentration of OH- ions in the solution under different pH conditions.

Since the initial solution is 0.048 M in Fe3+ and Zn2+, it implies that the concentration of OH- is equal to 3 times the concentration of Fe3+ (due to the stoichiometric ratio of Fe(OH)3).

Therefore, the initial OH- concentration is 0.144 M (3 * 0.048 M).

To find the approximate pH range, we can use the following equation:

pOH = -log[OH-]

pOH = -log(0.144)

pOH ≈ 0.84

To convert pOH to pH, we can use the equation:

pH = 14 - pOH

pH ≈ 14 - 0.84

Therefore, the approximate pH range suitable for the separation of Fe3+ and Zn2+ by precipitation of Fe(OH)3 is around 13.16 to 14.

Please note that this is an approximation and the actual pH range can vary based on experimental conditions. It is always recommended to conduct additional research and consult appropriate references for accurate results.