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Question

The elevation of the boiling point of 0.10m aqueous CrCl3.xNH3 solution is two times that of 0.05m aqueous CaCl2 solution. The value of x is……………..


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Solution

Elevation in boiling point:

  • Boiling point elevation refers to the increase in the boiling point of a solvent upon the addition of a solute.
  • When a non-volatile solute is added to a solvent, the resulting solution has a higher boiling point than that of the pure solvent.
  • For example, the boiling point of a solution of sodium chloride (salt) and water is greater than that of pure water.
  • The boiling point of a liquid is the temperature at which its vapor pressure is equal to the pressure of its surrounding environment.
  • Non-volatile substances do not readily undergo evaporation and have very low vapor pressures (assumed to be zero).
  • When a non-volatile solute is added to a solvent, the vapor pressure of the resulting solution is lower than that of the pure solvent.

The boiling point of a solution containing a non-volatile solute can be expressed as follows:

The boiling point of solution = boiling point of pure solvent + boiling point elevation (Tb).

The elevation in boiling point (Tb) is proportional to the concentration of the solute in the solution. It can be calculated via the following equation.

Tb=i×Kb×m

Where,

  • i is the Van't Hoff factor
  • Kb is the ebullioscopic constant
  • m is the molality of the solute

Calculate the value of x-

The molarity of the aqueous solution of CaCl2 is 0.05m.

And of CrCl3.xNH3 is 0.10m,

The expression used for the calculation of Vant Hoff's factor i,

The factor is given below:

Tb=i×Kb×mi×0.1×Kb=3×0.05×Kb×2i=3×0.05×Kb×20.1×Kbi=3×5100×2110×Kbi=3×10100×101i=3

To calculate the value of x the following reaction is used:

Cr(NH3)5ClCl2Cr(NH3)5Cl+2+2Clx=5

Hence, the elevation of the boiling point of 0.10m aqueous CrCl3.xNH3 solution is two times that of 0.05m aqueous CaCl2 solution. The value of x is 5.


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