When a solute is added to a solvent,the freezing point of the solution decreases to $1.86 \ K$. What is the value of $\Delta T_b$? $[K_f = 1.86, K_b = 0.512]$

$1 \, \text{mole}$ of liquid $A$ and $2 \, \text{moles}$ of liquid $B$ make a solution having an observed vapour pressure of $42 \, \text{torr}$. The vapour pressures of pure $A$ and pure $B$ are $45 \, \text{torr}$ and $36 \, \text{torr}$ respectively. The described solution:

The elevation in the boiling point of an aqueous urea solution is $0.104 \ K$. What is its $\Delta T_{f}$ (in $K$) value? (Given for water: $K_{b} = 0.52 \ K \ kg \ mol^{-1}$,$K_{f} = 1.86 \ K \ kg \ mol^{-1}$)

Which one of the following statements is false?

The $pH$ of a $0.1 \ M$ monobasic acid is $2$. Its osmotic pressure at a given temperature $T \ (K)$ is: (Given that the effective concentration for osmotic pressure is $(1+\alpha) \times$ concentration of acid, where $\alpha$ is the degree of dissociation)

$A$ solution has a $1:4$ mole ratio of pentane to hexane. The vapour pressure of the pure hydrocarbons at $20 \ ^oC$ are $440 \ mm \ Hg$ for pentane and $120 \ mm \ Hg$ for hexane. The mole fraction of pentane in the vapour phase would be