Question

A polymer sample contains 2 grams of molecular weight 10,000 and 4 grams of molecular weight 30,000. Calculate the polydispersity index of the sample.

Answer 1

Answer:

The polydispersity index of the sample is 1.16.

Explanation:

We are given that a polymer contains 2 grams of molecular weight 10,000 and 4 grams of molecular weight 30,000.

Therefore,  

The average number molecular weight,  

Mn =[ ∑Ni Mi ] / [∑Ni]

  = [(2 * 10,000) + (4 * 30,000)] / [2+4]

  = 140000 / 6

   = 23333.34

The weight number molecular weight,

Mw = [ ∑Ni Mi² ] / [ ∑Ni Mi ]

  = [{2*(10000)²} + {4*(30000)²}] / [(2*10,000)+(4* 30,000)]  

   = 10,000 [ (2*10000) + (4*90000)] / [140000]

    = 380000 / 14

     = 27142.85

Now, Polydispersity Index i.e.,

PDI = Mw/Mn = 27141.85/23333.34 = 1.16