Number of moles of Cul `(K_(sp) = 5 xx 10^(-12))` that will dissolve in 1 L of 0.1 M Nal solution is

Options

A. `2.2 xx 10^(-6)`
B. `5 xx 10^(-11)`
C. ` 5 xx 10^(-10)`
D. `2.2 xx 10^(-5)`

Answer

To solve the problem of how many moles of CuI will dissolve in 1 L of 0.1 M NaI solution, we can follow these steps:

### Step 1: Write the dissociation equation for CuI
CuI dissociates in water as follows:
\[ \text{CuI (s)} \rightleftharpoons \text{Cu}^+ (aq) + \text{I}^- (aq) \]

### Step 2: Define the solubility product constant (Ksp)
The solubility product constant (Ksp) for CuI is given as:
\[ K_{sp} = [\text{Cu}^+][\text{I}^-] = 5 \times 10^{-12} \]

### Step 3: Determine the concentration of iodide ions
Since we are dissolving CuI in a 0.1 M NaI solution, the concentration of iodide ions \([\text{I}^-]\) from NaI is:
\[ [\text{I}^-] = 0.1 \, \text{M} \]

### Step 4: Set up the expression for Ksp
Let \(s\) be the solubility of CuI in moles per liter. Upon dissolution, the concentration of copper ions \([\text{Cu}^+]\) will be \(s\) and the concentration of iodide ions will be \(0.1 + s\). However, since \(s\) is expected to be very small compared to 0.1, we can approximate:
\[ [\text{I}^-] \approx 0.1 \]

Thus, we can rewrite the Ksp expression as:
\[ K_{sp} = [\text{Cu}^+][\text{I}^-] = s \times 0.1 \]

### Step 5: Substitute Ksp value into the equation
Substituting the known values into the Ksp expression:
\[ 5 \times 10^{-12} = s \times 0.1 \]

### Step 6: Solve for s
Rearranging the equation to solve for \(s\):
\[ s = \frac{5 \times 10^{-12}}{0.1} = 5 \times 10^{-11} \]

### Step 7: Determine the number of moles
Since we are considering 1 L of solution, the number of moles of CuI that will dissolve is equal to \(s\):
\[ \text{Number of moles of CuI} = 5 \times 10^{-11} \, \text{moles} \]

### Final Answer
The number of moles of CuI that will dissolve in 1 L of 0.1 M NaI solution is:
\[ \text{5} \times 10^{-11} \, \text{moles} \]

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