# Which one of the following is the formula of weight average molecular mass$(\bar{M_w})$:-

$\begin{array}{1 1}(a)\;\large\frac{\sum m_iM_i}{\sum M_i}&(b)\; \large\frac{\sum m_iM_i}{\sum N_i}\\(c)\;\large\frac{\sum N_iM_i^2}{\sum N_iM_i}&(d)\;\large\frac{\sum N_iM_i}{\sum N_i}\end{array}$

If $m_1,m_2,m_3,.......$ are the masses of species with molecular masses $M_1,M_2,M_3.......$ respectively,then the weight average molecular mass is :
$\bar{M_w}=\large\frac{\sum m_iM_i}{m_i}$
$\Rightarrow \large\frac{\sum N_iM_i^2}{\sum N_iM_i}$
Hence (c) is the correct answer.