Respuesta :
The question is incomplete, the complete question is:
A certain substance X has a normal freezing point of [tex]-6.4^oC[/tex] and a molal freezing point depression constant [tex]K_f=3.96^oC.kg/mol[/tex]. A solution is prepared by dissolving some glycine in 950. g of X. This solution freezes at [tex]-13.6^oC[/tex] . Calculate the mass of urea that was dissolved. Round your answer to 2 significant digits.
Answer: The mass of glycine that can be dissolved is [tex]1.3\times 10^2g[/tex]
Explanation:
Depression in the freezing point is defined as the difference between the freezing point of the pure solvent and the freezing point of the solution.
The expression for the calculation of depression in freezing point is:
[tex]\text{Freezing point of pure solvent}-\text{freezing point of solution}=i\times K_f\times m[/tex]
OR
[tex]\text{Freezing point of pure solvent}=\text{Freezing point of solution}=i\times K_f\times \frac{m_{solute}\times 1000}{M_{solute}\times w_{solvent}\text{(in g)}}[/tex] ......(1)
where,
Freezing point of pure solvent = [tex]-6.4^oC[/tex]
Freezing point of solution = [tex]-13.6^oC[/tex]
i = Vant Hoff factor = 1 (for non-electrolytes)
[tex]K_f[/tex] = freezing point depression constant = [tex]3.96^oC/m[/tex]
[tex]m_{solute}[/tex] = Given mass of solute (glycine) = ?
[tex]M_{solute}[/tex] = Molar mass of solute (glycine) = 75.07 g/mol
[tex]w_{solvent}[/tex] = Mass of solvent = 950. g
Putting values in equation 1, we get:
[tex]-6.4-(-13.6)=1\times 3.96\times \frac{m_{solute}\times 1000}{75.07\times 950}\\\\m_{solute}=\frac{7.2\times 75.07\times 950}{1\times 3.96\times 1000}\\\\m_{solute}=129.66g=1.3\times 10^2g[/tex]
Hence, the mass of glycine that can be dissolved is [tex]1.3\times 10^2g[/tex]
