Question

What do you understand by the number average molecular mass of a polymer?

Answer 1

If a polymer is made of n₁ moles of molecular mass M₁, n₂ moles of molecular mass M₂, n₃ moles of molecular mass M₃, .... and so on, the number average molecular mass `(bar M_n)` is defined as 

`bar M_n =  (n_1M_1 + n_2M_2 + n_3M_3 + .....)/(n_1 + n_2 + n_3 + .....)`

= `(sum n_i M_i)/(sum n_i)`

where n_i is the number of moles having molecular mass M_i.

If N₁, N₂, N₃, ....., etc., are the corresponding number of molecules and N_a is the Avogadro number, we have

`bar M_n =  ((N_1//N_a) M_1 + (N_2//N_a) M_2 + (N_3//N_a) M_3 + ...)/((N_1//N_a) + (N_2//N_a) + (N_3//N_a) + ...)`

or, `bar M_n = (sum (N_i//N_a) M_i)/(sum N_i//N_a)`

or, `bar M_n = (sum N_i M_i)/(sum N_i)`

Where N_i is the number of molecules having molecular mass M_i.