The solubility product of `SrF_(2)` in water is `8xx10^(-10)` Calculate its solubility in 0.1 M of aqueous NaF solution. If its solubility is expressed as `y xx 10^(-8)` then what is the value of 'y' ?

Answer

To solve the problem, we will follow these steps:

### Step 1: Write the dissociation equation of SrF₂
The dissociation of strontium fluoride in water can be represented as:
\[ \text{SrF}_2 (s) \rightleftharpoons \text{Sr}^{2+} (aq) + 2\text{F}^- (aq) \]

### Step 2: Write the expression for the solubility product (Ksp)
The solubility product (Ksp) expression for SrF₂ is given by:
\[ K_{sp} = [\text{Sr}^{2+}][\text{F}^-]^2 \]

### Step 3: Define the solubility in pure water
Let the solubility of SrF₂ in pure water be \( s \). Therefore, at equilibrium:
- \([\text{Sr}^{2+}] = s\)
- \([\text{F}^-] = 2s\)

Substituting these into the Ksp expression:
\[ K_{sp} = s(2s)^2 = 4s^3 \]

### Step 4: Substitute the given Ksp value
We are given that \( K_{sp} = 8 \times 10^{-10} \):
\[ 4s^3 = 8 \times 10^{-10} \]

### Step 5: Solve for s
Rearranging the equation gives:
\[ s^3 = \frac{8 \times 10^{-10}}{4} = 2 \times 10^{-10} \]
Taking the cube root:
\[ s = \sqrt[3]{2 \times 10^{-10}} \]

### Step 6: Calculate the value of s
Calculating the cube root:
\[ s \approx 5.84 \times 10^{-4} \, \text{M} \]

### Step 7: Consider the effect of adding NaF
When NaF is added to the solution, it dissociates completely:
\[ \text{NaF} \rightarrow \text{Na}^+ + \text{F}^- \]
This means the concentration of \( \text{F}^- \) ions in the solution becomes \( 0.1 \, \text{M} + 2s \).

However, since \( s \) is very small compared to \( 0.1 \, \text{M} \), we can approximate:
\[ [\text{F}^-] \approx 0.1 \, \text{M} \]

### Step 8: Set up the Ksp expression with the new concentration
Now, substituting into the Ksp expression:
\[ K_{sp} = [\text{Sr}^{2+}][\text{F}^-]^2 \]
\[ 8 \times 10^{-10} = s(0.1)^2 \]
\[ 8 \times 10^{-10} = s(0.01) \]

### Step 9: Solve for s in the presence of NaF
Rearranging gives:
\[ s = \frac{8 \times 10^{-10}}{0.01} = 8 \times 10^{-8} \, \text{M} \]

### Step 10: Express s in the form y x 10^(-8)
Here, we can express the solubility as:
\[ s = 8 \times 10^{-8} \]

Thus, the value of \( y \) is:
\[ y = 8 \]

### Final Answer
The value of \( y \) is **8**.