The key difference between number average and weight average molecular weight is that the number average molecular weight refers to the mole fraction of molecules in a polymer sample whereas the weight average molecular weight is the weight fraction of molecules in a polymer sample.
Unlike pure compounds, polymers form as a mixture of different molecules (pure compounds contain identical molecules, but polymers contain non-identical molecules). For example, a polymer sample may contain long carbon chains but with different chain lengths in each molecule. Therefore, we use different averages to express the polymer molecular weights. Number average molecular weight and weight average molecular weight are such two types.
CONTENTS
1. Overview and Key Difference
2. What is Number Average Molecular Weight
3. What is Weight Average Molecular Weight
4. Side by Side Comparison – Number Average vs Weight Average Molecular Weight in Tabular Form
5. Summary
What is Number Average Molecular Weight?
Number average molecular weight is the mole fraction of molecules in a polymer sample. It is a way of determining the molecular mass of a polymer. It gives the average of the molecular masses of the individual macromolecules. In other words, it is the total weight of the sample divided by the number of molecules in the sample.
Figure 01: Weight average molecular weight is always greater than the number average molecular weight.
We can find the value of this parameter using the following equation:
Mn = ∑ NiMi / ∑ Ni
Here, Mn is the number average molecular weight, Ni is the number of molecules having Mi weight in the polymer sample, and Mi is the weight of a particular molecule of the sample. We can determine the number average molecular weight using gel permeation chromatography, viscometry and colligative methods such as vapour pressure osmometry.
What is Weight Average Molecular Weight?
Weight average molecular weight is the weight fraction of molecules in a polymer sample. It is another way of determining the molecular mass of a polymer. It gives the average of the molecular masses of the individual macromolecules in the polymer sample. We can find this parameter using the following equation:
Mw = ∑ NiMi2 / ∑ NiMi
Where Mw is the weight average molecular weight, Ni is the number of molecules of molecular mass Mi. We can determine this parameter using static light scattering, small angle neutron scattering, X-ray scattering, and sedimentation velocity. More importantly, the weight average molecular weight is always greater than the weight average molecular weight since larger molecules in a sample weigh more than smaller molecules.
What is the Difference Between Number Average and Weight Average Molecular Weight?
Since polymer samples contain molecules of different sizes, we cannot give the exact molecular weight of the polymer. Therefore, we use averages of different parameters to indicate the molecular weight of the polymer. The number average and weight average molecular weight are such two forms. The key difference between number average and weight average molecular weight is that the number average molecular weight refers to the mole fraction of molecules in a polymer sample whereas the weight average molecular weight is the weight fraction of molecules in a polymer sample. Another difference between number average and weight average molecular weight is that we can determine the number average molecular weight using gel permeation chromatography, viscometry and colligative methods such as vapour pressure osmometry while we can determine the weight average molecular weight using static light scattering, small angle neutron scattering, X-ray scattering, and sedimentation velocity.
The below infographic presents the difference between number average and weight average molecular weight in tabular form.
Summary – Number Average vs Weight Average Molecular Weight
The number average and weight average molecular weight are two parameters that we use to express the molecular weight of a polymer sample. The key difference between number average and weight average molecular weight is that the number average molecular weight refers to the mole fraction of molecules in a polymer sample whereas the weight average molecular weight is the weight fraction of molecules in a polymer sample.
Reference:
1. Libretexts. “Molecular Weights of Polymers.” Chemistry LibreTexts, Libretexts, 6 Sept. 2017. Available here
2. “Molar Mass Distribution.” Wikipedia, Wikimedia Foundation, 21 July 2018. Available here