Thank you for reporting, we will resolve it shortly
Q.
Mole fraction of glucose in aqueous solution is $0.5$. Hence, molality of glucose solution is
Some Basic Concepts of Chemistry
Solution:
Mole fraction of glucose $=0.5$
Hence, mole fraction of water $=0.5$
Thus, moles of water $=$ moles of glucose $=x$
Thus, water $=18 \,xg$
$=\frac{18 x }{1000} kg$
Molality $=\frac{\text { Moles of glucose }}{ kg \text { of } H _2 O } $
$=\frac{ X }{\frac{18 X }{1000}}=\frac{1000}{18}$
$=55.55 \,mol \,kg ^{-1}$
Direct Method
Molality $=\frac{1000 x _1(\text { glucose })}{\left(1- x _1\right) m_2(\text { water })}=\frac{1000 \times 0.5}{0.5 \times 18} $
$=55.55$