Say I'm given a mixture of batches of polydisperse polymers. I know the weight $w$, the number average $ \bar M_n$, and the weight average $ \bar M_w$ of each batch that was added to the final mixture. How would I go about calculating the $\bar M_w, \bar M_n$ and PD of the final mixture?
I'm thinking that the $\bar M_w$ value would simply be a weighted average of each of the batches, but I'm not quite sure how to get the number average.
In math, I'm thinking that $\bar M_{w,final} = \frac{\Sigma_{i} w_i \bar M_{w,i}}{\Sigma_i w_i} $
I haven't been able to reason what I should do to account for the differing numbers of molecules/moles of each batch. I think it should also be a weighted average, but using the numbers of each batch for weighting instead of the weight, but how would I calculate that?
Thank you