Question

If the ratio of the mole fraction of a solute is changed from $\frac{1}{3}$ to $\frac{1}{2}$ in the 800 g of solvent then the ratio of molality will be :

• A. 1 : 3
• B. 3 : 1
• C. 4 : 3
• D. 1 : 2

Answer 1

The correct option is D 1 : 2

Molality of solution is given by $\frac{{\chi }_A\times 1000}{(1-{\chi }_A)m_B}=m$.
Consider the molality for two different mole fraction i.e $\frac{1}{2}$,$\frac{1}{3}$ of $A$ be $m_1$ and $m_2$ respectively.
$m_1=\frac{\frac{1}{3}\times 1000}{(1-(\frac{1}{3}\left)\right)\times m_B}$....(i)
$m_2=\frac{\frac{1}{2}\times 1000}{(1-(\frac{1}{2}\left)\right)\times m_B}$....(ii)
On dividing equation (i) and (ii) we get
$\frac{m_1}{m_2}=1:2$