EMF of the following cell is 0.6 volt.
`Ag (s) | AgBr ( s) | KBr (0.01 m) |AgNO_(3) ( 0.001M) | Ag( s)`
`K_(sp)` of AgBr is expressed as `1 xx 10^(-x)` , x is [Take `( 2.303RT)/(F ) = 0.06 V ]`

Answer

To solve the problem, we need to find the solubility product constant (Ksp) of AgBr based on the given EMF of the cell. The cell is represented as:

\[ \text{Ag (s)} | \text{AgBr (s)} | \text{KBr (0.01 m)} | \text{AgNO}_3 (0.001M) | \text{Ag (s)} \]

### Step 1: Understand the Cell Reaction
The cell consists of two half-cells. The left half-cell involves the dissolution of AgBr, while the right half-cell involves the reduction of Ag+ ions. The overall cell reaction can be represented as:

\[ \text{AgBr (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Br}^- (aq) \]

### Step 2: Write the Nernst Equation
The Nernst equation relates the cell potential (E) to the concentrations of the reactants and products. It is given by:

\[ E = E^0 - \frac{RT}{nF} \ln Q \]

Where:
- \( E \) = cell potential (0.6 V)
- \( E^0 \) = standard cell potential
- \( R \) = universal gas constant (8.314 J/(mol·K))
- \( T \) = temperature in Kelvin (assume 298 K)
- \( n \) = number of moles of electrons transferred in the reaction
- \( F \) = Faraday's constant (96485 C/mol)
- \( Q \) = reaction quotient

### Step 3: Calculate Q
For the dissolution of AgBr, the reaction quotient \( Q \) can be expressed as:

\[ Q = \frac{[\text{Ag}^+][\text{Br}^-]}{1} \]

Given that the concentration of KBr is 0.01 M, we can assume that:

\[ [\text{Br}^-] = 0.01 \, \text{M} \]
\[ [\text{Ag}^+] = 0.001 \, \text{M} \]

Thus,

\[ Q = [\text{Ag}^+][\text{Br}^-] = (0.001)(0.01) = 1 \times 10^{-5} \]

### Step 4: Substitute Values into the Nernst Equation
Assuming \( E^0 \) is 0 (for simplicity, as we are looking for Ksp), we can rearrange the Nernst equation to find Ksp:

\[ 0.6 = 0 - \frac{(0.06)}{n} \log(1 \times 10^{-5}) \]

### Step 5: Determine n
In the dissolution of AgBr, one mole of AgBr produces one mole of Ag+ and one mole of Br-. Thus, \( n = 1 \).

### Step 6: Solve for Ksp
Now substituting \( n = 1 \):

\[ 0.6 = -0.06 \log(1 \times 10^{-5}) \]

Calculating \( \log(1 \times 10^{-5}) \):

\[ \log(1 \times 10^{-5}) = -5 \]

Now substituting back:

\[ 0.6 = -0.06 \times (-5) \]
\[ 0.6 = 0.3 \]

Now, we can find Ksp:

\[ Ksp = [\text{Ag}^+][\text{Br}^-] = (0.001)(0.01) = 1 \times 10^{-5} \]

### Step 7: Express Ksp in the Required Form
The problem states that Ksp is expressed as \( 1 \times 10^{-x} \). Here, \( x = 5 \).

Thus, the final answer is:

**x = 5**