Question

A solution is obtained by dissolving 0.2 moles of urea in a liter of water. Another solution is obtained by dissolving 0.4 moles of cane sugar in a liter of water at the same temperature. The lowering of vapor pressure to the first solution is:
A. same as that of second solution
B. half to that of second solution
C. double to that of second solution
D. none of the above

Answer 1

Hint Colligative properties are those properties of a solution that is dependent on the ratio between the total numbers of solute particles to the total number of solvent particles. These properties are not dependent on the chemical nature of the substance.

Complete Step by step solution:
Colligative properties include: Relative lowering of vapor pressure, elevation in boiling point, depression in freezing point and osmotic pressure.
Lowering of vapor pressure can be explained on the basis of non-volatile solute i.e. if a non-volatile solute is added to the solvent then fraction of surface which is covered with the solvent molecules gets reduced and at the same temperature the vapor pressure of the solution is lower as compared to pure solvent.
Lowering of vapor pressure can be calculated by the formula $ \Delta {{P}_{1}}={{X}_{solute}}P{{{}^\circ }_{solvent}} $ and in this case solvent given is water and $ {{X}_{solute}} $ is given as: $ \Delta {{P}_{1}}=\dfrac{{{n}_{urea}}}{total\text{ moles}}P{{{}^\circ }_{solvent}} $ , number of moles of urea is given as 0.2 by putting the value in equation we got
 $ \Delta {{P}_{1}}=\dfrac{0.2}{total\text{ moles}}P{{{}^\circ }_{solvent}} $
Similarly $ \Delta {{P}_{2}}=\dfrac{{{n}_{cane\ \text{sugar}}}}{total\text{ moles}}P{{{}^\circ }_{water}} $
Number of moles of cane sugar = 0.4
 $ \Delta {{P}_{2}}=\dfrac{0.4}{total\text{ moles}}P{{{}^\circ }_{water}} $
 $ \dfrac{\Delta {{P}_{1}}}{\Delta {{P}_{2}}}=\dfrac{1}{2} $
Which defines that \[\Delta {{P}_{1}}=\dfrac{1}{2}\Delta {{P}_{2}}\] i.e. the lowering of vapor pressure to the first solution is half to that of second solution.

Thus option B is the correct answer.

Note: Solution is a homogeneous mixture of two components called solute and solvent where solute is that substance which gets dissolved and solvent is that substance in which solute is dissolved and they both make a solution.