Answer :
Answer: The molar mass of the sample is 120.6 g/mol
Explanation:
To calculate the depression in freezing point, we use the equation:
[tex]\Delta T_f=iK_fm[/tex]
Or,
[tex]\Delta T_f=i\times K_f\times \frac{m_{solute}\times 1000}{M_{solute}\times W_{solvent}\text{ (in grams)}}[/tex]
where,
[tex]\Delta T_f[/tex] = depression in freezing point = 0.42°C
i = Vant hoff factor = 1 (For non-electrolytes)
[tex]K_f[/tex] = molal freezing point elevation constant = 5.065°C/m
[tex]m_{solute}[/tex] = Given mass of solute (sample) = 0.500 g
[tex]M_{solute}[/tex] = Molar mass of solute (sample) = ? g/mol
[tex]W_{solvent}[/tex] = Mass of solvent (benzene) = 50.0 g
Putting values in above equation, we get:
[tex]0.42^oC=1\times 5.065^oC/m\times \frac{0.500\times 1000}{M_{solute}\times 50.0}\\\\M_{solute}=\frac{1\times 5.065\times 0.500\times 1000}{50.0\times 0.42}=120.6g/mol[/tex]
Hence, the molar mass of the sample is 120.6 g/mol