Calculate $\Delta T_{f}$ of aqueous $0.01 \ m$ formic acid if the van't Hoff factor is $1.1$. $[K_{f} = 1.86 \ K \ kg \ mol^{-1}]$ (in $K$)

Freezing point of a $4 \%$ aqueous solution of $X$ is equal to the freezing point of a $12 \%$ aqueous solution of $Y$. If the molecular weight of $X$ is $A$,then the molecular weight of $Y$ is ............. $A$.

$A$ camphor sample melts at $176^{\circ} C$. $K_f$ for camphor is $40 \ K \ kg \ mol^{-1}$. $A$ solution of $0.02 \ g$ of a hydrocarbon in $0.8 \ g$ of camphor melts at $156.77^{\circ} C$. The hydrocarbon is made up of $92.3 \%$ of carbon. What is the molecular formula of the hydrocarbon?

If $0.072 \ g-atom$ of sulfur is dissolved in $100 \ g$ of solvent $(K_f = 7.00)$,the depression in freezing point is $0.84 \ ^\circ C$. The molecular formula of sulfur in the solution is .............

The freezing point of a solution containing $1.25 \ g$ of a non-electrolyte solute in $20 \ g$ of water is $271.9 \ K$. What is the molar mass of the solute? (Given: $K_f$ for water = $1.86 \ K \ kg \ mol^{-1}$,Freezing point of pure water = $273 \ K$)

If the $K_f$ value of $H_2O$ is $1.86 \ K \ kg \ mol^{-1}$,the value of $\Delta T_f$ for a $0.1 \ m$ solution of a non-volatile solute is: