Question

The boiling point of benzene is 353.23K. When 1.80 gram of non-volatile solute was dissolved in 90 gram of benzene . The boiling is raised to 354.11K. Calculate the molar mass of solute. $({{K}_{b}}$ for benzene = 2.53K/mol)

Answer 1

Hint: Boiling point elevation is that the difference between the ultimate and initial temperature. The boiling point elevation is directly proportional to the molar concentration(amount of substance per mass) of the answer. Molar mass is the mass of all atoms of a molecule in grams per mole. . The molar mass is the mass of a given element or compound (g) divided by the number of substances (mol).
Formula used:
${{M}_{2}}=\dfrac{{{K}_{b}}\times {{w}_{2}}\times 1000}{\vartriangle {{T}_{b}}\times {{w}_{_{1}}}}$
Where, ${{M}_{2}}$ is the molar mass of solute.
${{K}_{b}}$ is the boiling point elevation constant.

Complete answer:
The elevation in the boiling point ,
$\vartriangle {{T}_{_{b}}}={{T}_{b(solution)}}-{{T}_{b(solute)}}$
Substituting the values of ${{T}_{b(solution)}}\And {{T}_{b(solute)}}$ we get,
$\vartriangle {{T}_{b}}=354.11-353.23=0.88K$
The equation for the molar mass of the solute is,
${{M}_{2}}=\dfrac{{{K}_{b}}\times {{w}_{2}}\times 1000}{\vartriangle {{T}_{b}}\times {{w}_{_{1}}}}$
Where, ${{M}_{2}}$ is the molar mass of solute.
${{K}_{b}}$ is the molal boiling point elevation constant.
Substituting the values in the above expression,
${{M}_{2}}=\dfrac{2.53\times 1.8\times 1000}{0.88\times 90}=57.5g/mol$
Hence the molar mass of solute is 57.5g/mol.

Additional information:
Boiling is that the process by which liquid turns into a vapor when it's heated to its boiling point. The change from a liquid phase to a gaseous phase occurs when the vapor pressure of the liquid is capable the atmospheric pressure exerted on the liquid
The process of changing liquid into a vapor is called boiling . The change from a liquid phase to a gaseous phase occurs when the vapor pressure of the liquid is capable of the atmospheric pressure exerted on the liquid.

Note:
Benzene features a boiling point of 80.1degree celsius and freezing point of 5.5 degree Centigrade and it's soluble in organic solvents, but only slightly soluble in water. Also the elevation in boiling point is typically directly proportional to molal concentration of the solute dissolved in the solvent.