Answer :
To calculate the solubility of Iron(II) carbonate (FeCO₃) in water given its solubility product constant (Ksp) of [tex]\(3.13 \times 10^{-11}\)[/tex], we can follow these steps:
### Step-by-Step Solution:
1. Understanding the Dissociation:
Iron(II) carbonate (FeCO₃) dissociates in water as follows:
[tex]\[ \text{FeCO}_3 (s) \leftrightarrow \text{Fe}^{2+} (aq) + \text{CO}_3^{2-} (aq) \][/tex]
2. Define the Solubility:
Let [tex]\( s \)[/tex] be the molar solubility of FeCO₃ in water, i.e., the number of moles of FeCO₃ that dissolve per liter.
3. Express the Ion Concentrations:
When FeCO₃ dissolves, it produces one Fe²⁺ ion and one CO₃²⁻ ion for each formula unit of FeCO₃:
[tex]\[ [\text{Fe}^{2+}] = s \][/tex]
[tex]\[ [\text{CO}_3^{2-}] = s \][/tex]
4. Write the Solubility Product Expression:
The solubility product constant (Ksp) for FeCO₃ is given by:
[tex]\[ \text{Ksp} = [\text{Fe}^{2+}][\text{CO}_3^{2-}] \][/tex]
Substitute the concentrations of the ions in terms of [tex]\( s \)[/tex]:
[tex]\[ \text{Ksp} = s \times s \][/tex]
[tex]\[ \text{Ksp} = s^2 \][/tex]
5. Solve for [tex]\( s \)[/tex]:
Given the Ksp value of [tex]\( 3.13 \times 10^{-11} \)[/tex]:
[tex]\[ 3.13 \times 10^{-11} = s^2 \][/tex]
[tex]\[ s = \sqrt{3.13 \times 10^{-11}} \][/tex]
6. Calculate the Solubility:
Perform the square root calculation:
[tex]\[ s = \sqrt{3.13 \times 10^{-11}} \][/tex]
[tex]\[ s \approx 5.594 \times 10^{-6} \, \text{M} \][/tex]
Therefore, the solubility of FeCO₃ in water is approximately [tex]\( 5.59 \times 10^{-6} \, \text{M} \)[/tex].
### Conclusion:
Among the given options, the value that matches our calculated solubility is:
[tex]\[ 5.59 \times 10^{-6} \, \text{M} \][/tex]
So, the correct answer is [tex]\( 5.59 \times 10^{-6} \, \text{M} \)[/tex].
### Step-by-Step Solution:
1. Understanding the Dissociation:
Iron(II) carbonate (FeCO₃) dissociates in water as follows:
[tex]\[ \text{FeCO}_3 (s) \leftrightarrow \text{Fe}^{2+} (aq) + \text{CO}_3^{2-} (aq) \][/tex]
2. Define the Solubility:
Let [tex]\( s \)[/tex] be the molar solubility of FeCO₃ in water, i.e., the number of moles of FeCO₃ that dissolve per liter.
3. Express the Ion Concentrations:
When FeCO₃ dissolves, it produces one Fe²⁺ ion and one CO₃²⁻ ion for each formula unit of FeCO₃:
[tex]\[ [\text{Fe}^{2+}] = s \][/tex]
[tex]\[ [\text{CO}_3^{2-}] = s \][/tex]
4. Write the Solubility Product Expression:
The solubility product constant (Ksp) for FeCO₃ is given by:
[tex]\[ \text{Ksp} = [\text{Fe}^{2+}][\text{CO}_3^{2-}] \][/tex]
Substitute the concentrations of the ions in terms of [tex]\( s \)[/tex]:
[tex]\[ \text{Ksp} = s \times s \][/tex]
[tex]\[ \text{Ksp} = s^2 \][/tex]
5. Solve for [tex]\( s \)[/tex]:
Given the Ksp value of [tex]\( 3.13 \times 10^{-11} \)[/tex]:
[tex]\[ 3.13 \times 10^{-11} = s^2 \][/tex]
[tex]\[ s = \sqrt{3.13 \times 10^{-11}} \][/tex]
6. Calculate the Solubility:
Perform the square root calculation:
[tex]\[ s = \sqrt{3.13 \times 10^{-11}} \][/tex]
[tex]\[ s \approx 5.594 \times 10^{-6} \, \text{M} \][/tex]
Therefore, the solubility of FeCO₃ in water is approximately [tex]\( 5.59 \times 10^{-6} \, \text{M} \)[/tex].
### Conclusion:
Among the given options, the value that matches our calculated solubility is:
[tex]\[ 5.59 \times 10^{-6} \, \text{M} \][/tex]
So, the correct answer is [tex]\( 5.59 \times 10^{-6} \, \text{M} \)[/tex].
