Respuesta :
To answer this question, we have to use the formula of the cryoscopic descent:
[tex]\Delta T_c=k_f\cdot m[/tex]Where ΔTc is the difference between the freezing points of the pure solvent and the solution, kf is the cryoscopic constant (that for water it has a value of 1.86°C*kg/mol and m is the molality of the solution.
The first step we have to follow is to find the molality of the solution using this formula and the given values.
Estimate the difference between the freezing point of the water and the one of the solution:
[tex]\Delta T_c=0\degree C-(-0.435\degree C)=0.435\degree C[/tex][tex]\begin{gathered} 0.435\degree C=1.86\degree Ckg/mol\cdot m \\ m=\frac{0.435\degree C}{1.86\degree Ckg/mol} \\ m=0.234mol/kg \end{gathered}[/tex]The molality of the solution is 0.234mol/kg.
Now we have to use this molality to find the amount of moles present in the solution.
Molality equals moles of solute/kg of solvent. We know that there are 95.0g of solvent, by converting this mass to kg and using the molality we can find the amount of moles of solute present in the solution, this way:
[tex]95.0g\cdot\frac{1kg}{1000g}=0.095kg[/tex][tex]0.095kg\cdot\frac{0.234mol}{kg}=0.02223mol[/tex]It means that there are 0.02223 moles of solute in the solution.
Our last step to answer this question is to divide the mass of solute present in the solution by the amount of moles of it to find its molar mass:
[tex]\frac{2.49g}{0.02223mol}=112.01g/mol[/tex]It means that the molar mass of the solute is 112.01g/mol.
