If`N_(1),N_(2),N_(3),……`are the number of molcules with molecular masses `M_(1),M_(2),(M_(3),…`respectively ,then mass average molar mass is expressed as:

Options

A. `(N_(1)M_(1)^(2),N_(2)M_(2)^(2),+……)/((N_(1)M_(1),N_(2)M_(2),+……))=(SigmaNiMi^(2))/(SigmaNiMi)`
B. `(N_(1)M_(1),N_(2)M_(2),+……)/((N_(1),N_(2),+……))=(SigmaNiMi)/(SigmaNi)`
C. `(SigmaMi^(2))/(SigmaNi)`
D. `(SigmaNiMi)/(SigmaMi)`

Answer

To find the mass average molar mass given the number of molecules and their respective molecular masses, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Variables**:
- Let \( N_1, N_2, N_3, \ldots \) be the number of molecules.
- Let \( M_1, M_2, M_3, \ldots \) be the respective molecular masses of these molecules.

2. **Identify the Formula for Mass Average Molar Mass**:
- The mass average molar mass (also known as weight average molecular mass) is calculated using the formula:
\[ \bar{M}_w = \frac{\sum (N_i \cdot M_i^2)}{\sum (N_i \cdot M_i)} \]
where \( \bar{M}_w \) is the mass average molar mass, \( N_i \) is the number of molecules, and \( M_i \) is the molecular mass of each type of molecule.

3. **Calculate the Numerator**:
- The numerator is the sum of the products of the number of molecules and the square of their respective molecular masses:
\[ \text{Numerator} = N_1 \cdot M_1^2 + N_2 \cdot M_2^2 + N_3 \cdot M_3^2 + \ldots \]

4. **Calculate the Denominator**:
- The denominator is the sum of the products of the number of molecules and their respective molecular masses:
\[ \text{Denominator} = N_1 \cdot M_1 + N_2 \cdot M_2 + N_3 \cdot M_3 + \ldots \]

5. **Combine the Results**:
- Finally, substitute the results from the numerator and denominator into the formula to get the mass average molar mass:
\[ \bar{M}_w = \frac{N_1 \cdot M_1^2 + N_2 \cdot M_2^2 + N_3 \cdot M_3^2 + \ldots}{N_1 \cdot M_1 + N_2 \cdot M_2 + N_3 \cdot M_3 + \ldots} \]

### Final Answer:
The mass average molar mass is expressed as:
\[ \bar{M}_w = \frac{\sum (N_i \cdot M_i^2)}{\sum (N_i \cdot M_i)} \]