Molecular Masses and Colligative Properties

What is molar mass of solute if solution prepared by dissolving $0.822 \mathrm{gm}$ of it in $300 {\mathrm{cm}}^3$ of water has an osmotic pressure $149 \mathrm{mm}$ $\mathrm{Hg}$ at $248 \mathrm{K}$?

Determine the osmotic pressure of $5\%$ glucose solution at ${25}^{\circ }\mathrm{C}$. Molecular mass of glucose$=180 \mathrm{g}$, $\mathrm{R}=0.0821 \mathrm{L} \mathrm{atm} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$.

The osmotic pressure of $0.2$ molar solution of urea at $300 \mathrm{K}$ $\left(\mathrm{R}=0.082 \mathrm{L} \mathrm{atm} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)$ is

Define elevation in boiling point. How can you calculate the molecular mass of a non-volatile solute with it ?

An aqueous solution of volume $300 {\mathrm{cm}}^3$ contains $0.63 \mathrm{g}$ of protein. The osmotic pressure of the solution at $300 \mathrm{K}$ is $1.29 \mathrm{mbar}$. The molar mass of the protein is ${\mathrm{gmol}}^{-1}$.

Given : $\mathrm{R}=0.083 {\mathrm{L}}_{\mathrm{bar}}{\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$

$60 \mathrm{g}$ of a non-volatile solid $\mathrm{AB}$(having crystals like $\mathrm{NaCl}$) is dissolved in $0.50 \mathrm{kg}$ water. The normal boiling point of solution is found to be $102.08°\mathrm{C}$. The molal elevation of water is $0.52 \mathrm{K}-\mathrm{kg} {\mathrm{mol}}^{-1}$. The density of solid $\mathrm{AB}$ is $6.25 \mathrm{g}/{\mathrm{cm}}^3$ and the edge-length of unit cell is $400 \mathrm{pm}$. The effective number of atoms per unit cell is (Use Avogadro's number $=6\times {10}^{23}$)

$2\mathrm{g}$ of non-electrolyte solute dissolved in $200\mathrm{g}$ of water shows an elevation of boiling point of $0.{026}^{\mathrm{o}}\mathrm{C}$. ${\mathrm{K}}_{\mathrm{b}}$ of water is $0.52\mathrm{K}. {\mathrm{mole}}^{-1} \mathrm{Kg}$ then the molecular weight of solute is $\mathrm{x}\times 100$. What is the value of '$\mathrm{x}$'?

An aqueous solution containing $3 \mathrm{g}$ of a solute of molar mass $111.6 \mathrm{g} {\mathrm{mol}}^{-1}$ in a certain mass of water freezes at $-0.{125}^{\circ }\mathrm{C}$. The mass of water in grams present in the solution is $\left({\mathrm{K}}_{\mathrm{f}}=1.86 \mathrm{K} \mathrm{kg} {\mathrm{mol}}^{-1}\right)$

When 1 g of arsenic is added to $80 \mathrm{g}$ of benzene, the freezing point of benzene is lowered by $0.19°\mathrm{C} ({\mathrm{K}}_{\mathrm{f}} = 4.9)$. The formula of arsenic is ($\mathrm{At}. \mathrm{wt}. \mathrm{of} \mathrm{As} = 75$).

A solution containing $5 \%$  urea  solution (molecular mass = 60 g mol^-1) is isotonic with a 20 % solution of a nonvolatile solute. The molar mass of non volatile solute is-

What do you understand by relative lowering of vapour pressure? How it is used to determine the molecular mass of the solute?

$\mathrm{Calculate} \mathrm{the} \mathrm{mass} \mathrm{of} \mathrm{compound} (\mathrm{molar} \mathrm{mass} = 256 \mathrm{g} {\mathrm{mol}}^{-1}) \mathrm{to} \mathrm{be} \mathrm{dissolved} \mathrm{in} 75 \mathrm{g} \mathrm{of} \mathrm{benzene} \mathrm{to} \mathrm{lower} \mathrm{its} \mathrm{freezing} \mathrm{point} \mathrm{by} 0.48 \mathrm{K} ({\mathrm{K}}_{\mathrm{f}}= 5.12 \mathrm{K} \mathrm{kg} {\mathrm{mol}}^{-1})$

$15 \mathrm{g} \mathrm{of} \mathrm{an} \mathrm{unknown} \mathrm{molecular} \mathrm{substance} \mathrm{was} \mathrm{dissolved} \mathrm{in} 450 \mathrm{g} \mathrm{of} \mathrm{water}. \mathrm{The} \mathrm{resulting} \mathrm{solution} \mathrm{freezes} \mathrm{at} -0.34°\mathrm{C}. \mathrm{What} \mathrm{is} \mathrm{the} \mathrm{molar} \mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{substance} ? ({\mathrm{K}}_{\mathrm{f}} \mathrm{for} \mathrm{water} = 1.86 \mathrm{K} \mathrm{kg} {\mathrm{mol}}^{-1}).$

$\mathrm{What} \mathrm{mass} \mathrm{of} \mathrm{ethylene} \mathrm{glycol} (\mathrm{molar} \mathrm{mass} = 62.0 \mathrm{g} {\mathrm{mol}}^{-1}) \mathrm{must} \mathrm{be} \mathrm{added} \mathrm{to} 5.50 \mathrm{kg} \mathrm{of} \mathrm{water} \mathrm{to} \mathrm{lower} \mathrm{the} \mathrm{freezing} \mathrm{point} \mathrm{of} \mathrm{water} \mathrm{from} 0°\mathrm{C} \mathrm{to} -10.0°\mathrm{C} ({\mathrm{K}}_{\mathrm{f}} \mathrm{for} \mathrm{water} = 1.86 \mathrm{K} \mathrm{kg} {\mathrm{mol}}^{-1}).$

$\mathrm{The} \mathrm{molal} \mathrm{freezing} \mathrm{point} \mathrm{depression} \mathrm{constant} \mathrm{of} \mathrm{benzene} \left({\mathrm{C}}_6{\mathrm{H}}_6\right) \mathrm{is} 4.90 \mathrm{K} \mathrm{kg} {\mathrm{mol}}^{-1}. \mathrm{Selenium} \mathrm{exists} \mathrm{as} \mathrm{a} \mathrm{polymer} \mathrm{of} \mathrm{the} \mathrm{type} {\mathrm{Se}}_{\mathrm{x}}.\mathrm{When} 3.26 \mathrm{g} \mathrm{of} \mathrm{selenium} \mathrm{is} \mathrm{dissolved} \mathrm{in} 226 \mathrm{g} \mathrm{of} \mathrm{benzene}, \mathrm{the} \mathrm{observed} \mathrm{freezing} \mathrm{point} \mathrm{is} 0.112°\mathrm{C} \mathrm{lower} \mathrm{than} \mathrm{for} \mathrm{pure} \mathrm{benzene}. \mathrm{Deduce} \mathrm{the} \mathrm{molecular} \mathrm{formula} \mathrm{of} \mathrm{selenium} (\mathrm{At}. \mathrm{mass} \mathrm{of} \mathrm{Se} = 78.8 \mathrm{g} {\mathrm{mol}}^{-1}).$

$\mathrm{Vapour} \mathrm{pressure} \mathrm{of} \mathrm{water} \mathrm{at} 293 \mathrm{K} \mathrm{is} 17.51 \mathrm{mm}. \mathrm{Lowering} \mathrm{of} \mathrm{vapour} \mathrm{pressure} \mathrm{of} \mathrm{a} \mathrm{sugar} \mathrm{is} 0.0614 \mathrm{mm}. \mathrm{Calculate} \mathrm{the} \mathrm{mole} \mathrm{fraction} \mathrm{of} \mathrm{water}.$

$\mathrm{Addition} \mathrm{of} 0.643 \mathrm{g} \mathrm{of} \mathrm{a} \mathrm{compound} \mathrm{to} 50 \mathrm{ml} \mathrm{of} \mathrm{benzene} (\mathrm{density} : 0.879 \mathrm{g}/\mathrm{ml}) \mathrm{lowers} \mathrm{the} \mathrm{freezing} \mathrm{point} \mathrm{from} 5.51°\mathrm{C} \mathrm{to} 5.03°\mathrm{C}. \mathrm{If} \mathrm{Ky} \mathrm{for} \mathrm{benzene} \mathrm{is} 5.12, \mathrm{calculate} \mathrm{the} \mathrm{molecular} \mathrm{weight} \mathrm{of} \mathrm{the} \mathrm{compound}.$

$\mathrm{Pure} \mathrm{solvent} \mathrm{A} \mathrm{has} \mathrm{freezing} \mathrm{point} 16.5°\mathrm{C}. \mathrm{On} \mathrm{dissolving} 0.4 \mathrm{g} \mathrm{of} \mathrm{B} \mathrm{in} 200 \mathrm{g} \mathrm{of} \mathrm{A}, \mathrm{the} \mathrm{solution} \mathrm{freezes} \mathrm{at} 16.4°\mathrm{C} \mathrm{and} \mathrm{on} \mathrm{dissolving} 2.24 \mathrm{g} \mathrm{of} \mathrm{C} \mathrm{in} 100 \mathrm{g} \mathrm{of} \mathrm{A}, \mathrm{the} \mathrm{solution} \mathrm{has} \mathrm{freezing} \mathrm{point} \mathrm{of} 16.0°\mathrm{C}. \mathrm{If} \mathrm{the} \mathrm{molar} \mathrm{mass} \mathrm{of} \mathrm{B} \mathrm{is} 74 \mathrm{g} {\mathrm{mol}}^{-1}, \mathrm{what} \mathrm{is} \mathrm{the} \mathrm{molar} \mathrm{mass} \mathrm{of} \mathrm{C} ?$