Question

Mole fraction of glucose in aqueous solution is $0.5$. Hence, molality of glucose solution is

• A. $55.55$
• B. $1.0$
• C. $0.055$
• D. $90.0$

Answer 1

Answer: (A)

Mole fraction of glucose $=0.5$
Hence, mole fraction of water $=0.5$
Thus, moles of water $=$ moles of glucose $=x$
Thus, water $=18xg$
$=\frac{18x}{1000}kg$
Molality $=\frac{\text{ Moles of glucose }}{kg\text{ of }{H}_{2}O}$
$=\frac{X}{\frac{18X}{1000}}=\frac{1000}{18}$
$=55.55molk{g}^{-1}$
Direct Method
Molality $=\frac{1000x_1(\text{ glucose })}{\left(1-x_1\right)m_2(\text{ water })}=\frac{1000\times 0.5}{0.5\times 18}$
$=55.55$