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Sagot :
Certainly! Let's solve the problem step-by-step for each scenario:
1. Solubility of Calcium Chloride (CaCl2) in Distilled Water:
Given the solubility product constant (Ksp) of Calcium Chloride, [tex]\( K_{sp} = 2.0 \times 10^{-9} \)[/tex].
The dissolution reaction of CaCl2 in water is:
[tex]\[ \text{CaCl}_2(s) \rightleftharpoons \text{Ca}^{2+}(aq) + 2\text{Cl}^-(aq) \][/tex]
Let the solubility of CaCl2 in water be [tex]\( S \)[/tex] mol/L. Then, the molar concentrations at equilibrium will be:
[tex]\[ [\text{Ca}^{2+}] = S \quad \text{and} \quad [\text{Cl}^-] = 2S \][/tex]
Substituting these into the expression for Ksp:
[tex]\[ K_{sp} = [\text{Ca}^{2+}][\text{Cl}^-]^2 = S \times (2S)^2 = S \times 4S^2 = 4S^3 \][/tex]
Therefore:
[tex]\[ 4S^3 = 2.0 \times 10^{-9} \][/tex]
Solving for [tex]\( S \)[/tex]:
[tex]\[ S^3 = \frac{2.0 \times 10^{-9}}{4} = 0.5 \times 10^{-9} = 5.0 \times 10^{-10} \][/tex]
[tex]\[ S = (5.0 \times 10^{-10})^{1/3} \][/tex]
Using the previously obtained result, the solubility [tex]\( S \)[/tex] in distilled water is approximately:
[tex]\[ S \approx 0.0007937005259841001 \text{ mol/L} \][/tex]
2. Solubility of Calcium Chloride (CaCl2) in a Solution of [tex]\( g \)[/tex] / 100 mL Calcium Fluoride (CaF2):
To calculate the solubility in [tex]\( g / 100 \text{ mL} \)[/tex], we need specific information about the concentration of CaF2. However, since this information is not provided, we cannot compute this value without additional data.
3. Solubility of Calcium Chloride (CaCl2) in 0.1 N Silver Chloride (AgCl) Solution:
The presence of AgCl can create a common ion effect where the [tex]\( \text{Cl}^- \)[/tex] concentration increases due to the dissociation:
[tex]\[ \text{AgCl}(s) \rightleftharpoons \text{Ag}^+(aq) + \text{Cl}^-(aq) \][/tex]
However, without additional specific data about the solubility product of AgCl or the actual concentration values of [tex]\( \text{Cl}^- \)[/tex] and [tex]\( \text{Ag}^+ \)[/tex], we cannot compute the solubility of CaCl2 in this context. More detailed information is required for an exact solution.
In conclusion, the solubility of Calcium Chloride (CaCl2) in distilled water is approximately [tex]\( 0.0007937005259841001 \)[/tex] mol/L, while the other cases cannot be precisely solved without additional information.
1. Solubility of Calcium Chloride (CaCl2) in Distilled Water:
Given the solubility product constant (Ksp) of Calcium Chloride, [tex]\( K_{sp} = 2.0 \times 10^{-9} \)[/tex].
The dissolution reaction of CaCl2 in water is:
[tex]\[ \text{CaCl}_2(s) \rightleftharpoons \text{Ca}^{2+}(aq) + 2\text{Cl}^-(aq) \][/tex]
Let the solubility of CaCl2 in water be [tex]\( S \)[/tex] mol/L. Then, the molar concentrations at equilibrium will be:
[tex]\[ [\text{Ca}^{2+}] = S \quad \text{and} \quad [\text{Cl}^-] = 2S \][/tex]
Substituting these into the expression for Ksp:
[tex]\[ K_{sp} = [\text{Ca}^{2+}][\text{Cl}^-]^2 = S \times (2S)^2 = S \times 4S^2 = 4S^3 \][/tex]
Therefore:
[tex]\[ 4S^3 = 2.0 \times 10^{-9} \][/tex]
Solving for [tex]\( S \)[/tex]:
[tex]\[ S^3 = \frac{2.0 \times 10^{-9}}{4} = 0.5 \times 10^{-9} = 5.0 \times 10^{-10} \][/tex]
[tex]\[ S = (5.0 \times 10^{-10})^{1/3} \][/tex]
Using the previously obtained result, the solubility [tex]\( S \)[/tex] in distilled water is approximately:
[tex]\[ S \approx 0.0007937005259841001 \text{ mol/L} \][/tex]
2. Solubility of Calcium Chloride (CaCl2) in a Solution of [tex]\( g \)[/tex] / 100 mL Calcium Fluoride (CaF2):
To calculate the solubility in [tex]\( g / 100 \text{ mL} \)[/tex], we need specific information about the concentration of CaF2. However, since this information is not provided, we cannot compute this value without additional data.
3. Solubility of Calcium Chloride (CaCl2) in 0.1 N Silver Chloride (AgCl) Solution:
The presence of AgCl can create a common ion effect where the [tex]\( \text{Cl}^- \)[/tex] concentration increases due to the dissociation:
[tex]\[ \text{AgCl}(s) \rightleftharpoons \text{Ag}^+(aq) + \text{Cl}^-(aq) \][/tex]
However, without additional specific data about the solubility product of AgCl or the actual concentration values of [tex]\( \text{Cl}^- \)[/tex] and [tex]\( \text{Ag}^+ \)[/tex], we cannot compute the solubility of CaCl2 in this context. More detailed information is required for an exact solution.
In conclusion, the solubility of Calcium Chloride (CaCl2) in distilled water is approximately [tex]\( 0.0007937005259841001 \)[/tex] mol/L, while the other cases cannot be precisely solved without additional information.
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