A polymer contains 30% molecules with molecular mass 20,000, 40% have 30,000 and rest have 60,000. Its `bar(M)n` is `36 xx 10^(x)`. What is x.

Explanation

To find the number average molecular weight (\( \bar{M}_n \)) of the polymer, we can follow these steps:

### Step 1: Identify the molecular masses and their percentages
- Molecular mass \( M_1 = 20,000 \) with percentage \( n_1 = 30\% \)
- Molecular mass \( M_2 = 30,000 \) with percentage \( n_2 = 40\% \)
- Molecular mass \( M_3 = 60,000 \) with percentage \( n_3 = 100\% - (30\% + 40\%) = 30\% \)

### Step 2: Convert percentages to fractions
- \( n_1 = 0.30 \)
- \( n_2 = 0.40 \)
- \( n_3 = 0.30 \)

### Step 3: Use the formula for number average molecular weight
The formula for number average molecular weight (\( \bar{M}_n \)) is given by:
\[ \bar{M}_n = \frac{(n_1 \cdot M_1) + (n_2 \cdot M_2) + (n_3 \cdot M_3)}{n_1 + n_2 + n_3} \]

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ \bar{M}_n = \frac{(0.30 \cdot 20,000) + (0.40 \cdot 30,000) + (0.30 \cdot 60,000)}{0.30 + 0.40 + 0.30} \]

### Step 5: Calculate the numerator
Calculating each term in the numerator:
- \( 0.30 \cdot 20,000 = 6,000 \)
- \( 0.40 \cdot 30,000 = 12,000 \)
- \( 0.30 \cdot 60,000 = 18,000 \)

Now sum these values:
\[ 6,000 + 12,000 + 18,000 = 36,000 \]

### Step 6: Calculate the denominator
The denominator is:
\[ 0.30 + 0.40 + 0.30 = 1.00 \]

### Step 7: Calculate \( \bar{M}_n \)
Now substituting back into the formula:
\[ \bar{M}_n = \frac{36,000}{1.00} = 36,000 \]

### Step 8: Express \( \bar{M}_n \) in scientific notation
We can express \( 36,000 \) in scientific notation:
\[ 36,000 = 36 \times 10^3 \]

### Step 9: Identify \( x \)
From the expression \( \bar{M}_n = 36 \times 10^x \), we can see that \( x = 3 \).

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{3} \]