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Question
What do you understand by the weight average molecular masses of a polymer?
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Solution
If a polymer consists of mass m1 of macromolecules of molecular mass M1, mass m2 of macromolecules of molecular mass M2, mass m3 of macromolecules of molecular mass M3, ......... and so on, the weight average molecular mass, `bar M_W`, is defined as
`bar M_W = (m_1M_1 + m_2M_2 + m_3M_3 + .....)/(m_1 + m_2 + m_3 + .....)`
= `(sum m_i M_i)/(sum m_i)` ...(i)
Where mi is the mass of the macromolecules whose molecular mass is Mi.
If n1, n2, n3, ...., etc., are the corresponding number of moles, then we have
m1 = n1 M1, m2 = n2 M2, m3 = n3 M3, ...., i.e., in general, mi = ni Mi.
Hence, from Eq. (i), we have,
`bar M_W = (sum n_i M_i * M_i)/(sum n_i M_i)`
or, `bar M_W = (sum n_i M_i^2)/(sum n_i M_i)` ...(ii)
Where ni is the number of moles of the macromolecule having molecular mass Mi. Further, if N1, N2, N3, ........, etc., are the corresponding number of molecules, Eq. (ii) can be written as,
`bar M_W = (sum N_i M_i^2)/(sum N_i M_i)`
Where Ni represents the number of molecules having molecular mass Mi.
