In a sample of a polymer, 100 molecules have molecular mass `10^(3)` each and 200 molecules have molecular mass `10^(4)` each, the Number average molecular weight of polymer is `x xx 10^(3)` then 'x' is

Explanation

To find the number average molecular weight of the polymer sample, we can use the formula for the number average molecular weight (M_n):

\[ M_n = \frac{(m_1 \cdot n_1) + (m_2 \cdot n_2)}{n_1 + n_2} \]

Where:
- \( m_1 \) and \( m_2 \) are the molecular masses of the two types of molecules.
- \( n_1 \) and \( n_2 \) are the number of molecules of each type.

### Step 1: Identify the values
From the problem:
- \( m_1 = 10^3 \) (molecular mass of the first type of molecule)
- \( n_1 = 100 \) (number of the first type of molecules)
- \( m_2 = 10^4 \) (molecular mass of the second type of molecule)
- \( n_2 = 200 \) (number of the second type of molecules)

### Step 2: Substitute the values into the formula
Substituting the values into the formula gives:

\[ M_n = \frac{(10^3 \cdot 100) + (10^4 \cdot 200)}{100 + 200} \]

### Step 3: Calculate the numerator
Calculating the numerator:

\[ 10^3 \cdot 100 = 10^5 \]
\[ 10^4 \cdot 200 = 2 \cdot 10^6 \]

Thus, the numerator becomes:

\[ 10^5 + 2 \cdot 10^6 = 10^5 + 20 \cdot 10^5 = 21 \cdot 10^5 \]

### Step 4: Calculate the denominator
The denominator is:

\[ 100 + 200 = 300 \]

### Step 5: Combine the results
Now, substituting back into the formula:

\[ M_n = \frac{21 \cdot 10^5}{300} \]

### Step 6: Simplify the expression
To simplify:

\[ M_n = \frac{21}{300} \cdot 10^5 \]

Calculating \( \frac{21}{300} \):

\[ \frac{21}{300} = \frac{7}{100} = 0.07 \]

Thus:

\[ M_n = 0.07 \cdot 10^5 = 7 \cdot 10^3 \]

### Step 7: Identify the value of \( x \)
From the expression \( M_n = x \cdot 10^3 \), we can see that \( x = 7 \).

### Final Answer
The value of \( x \) is \( 7 \).

---