Calculate the pH range required to separate 99.99% of Cr3+ from Zn2+ by precipitation of Cr(OH)3(s) in a solution that is initially 0.034 M in both Cr3+ and Zn2+. Use the Ksp values from Table 16.2 of Chang and calculate the pH to the nearest 0.01 pH unit.
Lowest pH=
Highest pH=
Isn't this the same type of problem as the AgBr and Ag3PO4?
To calculate the lowest and highest pH range required to separate 99.99% of Cr3+ from Zn2+, we need to determine the solubility product constant (Ksp) for Cr(OH)3 and Zn(OH)2 and use it to find the concentrations of Cr3+ and Zn2+ at different pH values.
1. Determine the Ksp values:
- From Table 16.2 of Chang, the Ksp values are:
- Ksp for Cr(OH)3 is 6.3 x 10^(-31)
- Ksp for Zn(OH)2 is 4.5 x 10^(-17)
2. Write down the precipitation reaction:
- Cr(OH)3(s) ⇌ Cr3+(aq) + 3OH-(aq)
- Zn(OH)2(s) ⇌ Zn2+(aq) + 2OH-(aq)
3. Calculate the concentration of OH- at different pH values:
- The concentration of OH- can be determined using the relation: [OH-] = 10^(-pOH)
- The pOH is the negative logarithm of the concentration of OH- ions.
4. Calculate the concentration of Cr3+ and Zn2+ at different pH values:
- At equilibrium, the concentration of Cr3+ and Zn2+ will depend on the concentration of OH-. We can use the solubility product equation to calculate their concentrations:
- For Cr3+: [Cr3+] = [OH-]^3 / Ksp for Cr(OH)3
- For Zn2+: [Zn2+] = [OH-]^2 / Ksp for Zn(OH)2
5. Calculate the pH values at which 99.99% of Cr3+ is precipitated:
- To determine the lowest pH, we assume that all Cr3+ is precipitated and calculate the OH- concentration required for that:
- [Cr3+] = 0.0001 * initial concentration of Cr3+
- [OH-] = (Ksp for Cr(OH)3 * [Cr3+] / 0.0001)^(1/3)
- Use the calculated [OH-] to find the corresponding pH value using the relation: pH = 14 - pOH.
6. Calculate the pH values at which 99.99% of Zn2+ remains dissolved:
- To determine the highest pH, we assume that all Zn2+ remains dissolved, and calculate the OH- concentration required for that:
- [Zn2+] = (1 - 0.9999) * initial concentration of Zn2+
- [OH-] = sqrt((Ksp for Zn(OH)2 * [Zn2+] / (1 - 0.9999)))
- Use the calculated [OH-] to find the corresponding pH value using the relation: pH = 14 - pOH.
7. Round the pH values to the nearest 0.01 pH unit to get the final answer.
Using this procedure, you can now calculate the lowest and highest pH range required to separate 99.99% of Cr3+ from Zn2+.