A solution containing 500 g of a protein per liter is isotonic with a solution containing 3.42 g sucrose per liter. The molecular mass of protein in 5 x `10^(x)`, hence x is.

Answer

To solve the problem, we need to find the molecular mass of the protein given that a solution containing 500 g of protein per liter is isotonic with a solution containing 3.42 g of sucrose per liter. We will use the concept of osmotic pressure to relate the two solutions.

### Step-by-Step Solution:

1. **Understand Isotonic Solutions**:
Isotonic solutions have the same osmotic pressure. Therefore, we can set the osmotic pressure of the protein solution equal to that of the sucrose solution.

2. **Write the Formula for Osmotic Pressure**:
The osmotic pressure (π) is given by the formula:
\[ \pi = C \cdot R \cdot T \]
where \(C\) is the concentration of the solution, \(R\) is the gas constant, and \(T\) is the temperature.

3. **Set Up the Equation**:
For the protein solution:
\[ \pi_{\text{protein}} = C_p \cdot R \cdot T \]
For the sucrose solution:
\[ \pi_{\text{sucrose}} = C_s \cdot R \cdot T \]
Since the two solutions are isotonic, we can equate them:
\[ C_p = C_s \]

4. **Express Concentration in Terms of Moles**:
The concentration \(C\) can be expressed as:
\[ C = \frac{n}{V} \]
where \(n\) is the number of moles and \(V\) is the volume of the solution. Given that the volume is 1 liter for both solutions, we have:
\[ C_p = \frac{n_p}{1} = n_p \quad \text{and} \quad C_s = \frac{n_s}{1} = n_s \]
Thus, we can write:
\[ n_p = n_s \]

5. **Calculate the Number of Moles**:
The number of moles \(n\) is given by:
\[ n = \frac{\text{mass}}{\text{molecular mass}} \]
For the protein:
\[ n_p = \frac{500 \, \text{g}}{M} \quad \text{(where M is the molecular mass of the protein)} \]
For sucrose:
\[ n_s = \frac{3.42 \, \text{g}}{342 \, \text{g/mol}} \quad \text{(molecular mass of sucrose is 342 g/mol)} \]

6. **Set the Number of Moles Equal**:
Since \(n_p = n_s\), we can set up the equation:
\[ \frac{500}{M} = \frac{3.42}{342} \]

7. **Cross-Multiply and Solve for M**:
Cross-multiplying gives:
\[ 500 \cdot 342 = 3.42 \cdot M \]
Simplifying this, we find:
\[ M = \frac{500 \cdot 342}{3.42} \]

8. **Calculate the Molecular Mass**:
Performing the calculation:
\[ M = \frac{171000}{3.42} \approx 50000 \, \text{g/mol} \]
This can be expressed as:
\[ M = 5 \times 10^4 \, \text{g/mol} \]

9. **Relate to Given Expression**:
The problem states that the molecular mass of the protein is \(5 \times 10^x\). We found \(M = 5 \times 10^4\), thus:
\[ x = 4 \]

### Final Answer:
The value of \(x\) is **4**.