Question

Pure Benzene boiled at ${80^ \circ }C$ . the boiling point of a solution containing 1 gram of substance dissolved in $83.4$ gram of benzene is ${80.175^ \circ }C$ . if the latent heat of vaporization of Benzene is $90\,cal\,per\,gram$ . Calculate the molecular mass of solute.

Answer 1

Hint: : In order to answer this question, you must recall the concepts of Solutions in which you have studied about colligative properties of solution and its formula including latent heat of vaporization. Use the correct formula to find the correct required answer. Use the correct units in calculations.


Complete answer:
A colligative property is a property of a solution that is dependent on the ratio between the total number of solute particles (in the solution) to the total number of solvent particles. Colligative properties are not dependent on the chemical nature of the solution’s components. Thus, colligative properties can be linked to several quantities that express the concentration of a solution, such as molarity, normality, and molality. The four colligative properties that can be exhibited by a solution are:
1) Boiling point elevation
2) Freezing point depression
3) Relative lowering of vapour pressure
4) Osmotic pressure
Step 2: In this step we will use the formulae to find our answer:
Boiling point of ${C_6}{H_{6\,}}\,\, = \,80 + 273\,\, = \,353K$
Latent heat of vaporization $({l_v})$$ = \,90\,cal/g$
$\Delta T\, = \,80.175 - 80\, = \,0.175$
$w\, = \,1\,g$
$W\, = \,83.4\,g$
${K_b}\, = \,\frac{{R{T^2}}}{{1000\, \times {l_v}}}$
${K_b}\, = $ Molal boiling point elevation constant
$ \Rightarrow \,{K_b}\, = \,\frac{{2 \times 353 \times 353}}{{1000 \times 90}}\, = \,2.769\,$
So , \[\Delta {T_b}\, = \,\,\frac{{{K_b} \times 1000 \times w}}{{m \times W}}\,\]
$ \Rightarrow \,0.175\, = \,\,\frac{{2.769 \times 1000 \times 1}}{{m \times 83.4}}\,$
$ \Rightarrow m\, = \,189.72\,g$
Hence, the required molecular mass of solute is, $m\, = \,189.72\,g$


Note: Latent heat is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition. Latent heat can be understood as energy in hidden form which is supplied or extracted to change the state of a substance without changing its temperature. Examples are latent heat of fusion and latent heat of vaporization involved in phase changes, i.e. a substance condensing or vaporizing at a specified temperature and pressure.