Answer : The molal freezing point depression constant of X is ![4.12^oC/m](/tpl/images/0390/6513/613fb.png)
Explanation : Given,
Mass of urea (solute) = 5.90 g
Mass of X liquid (solvent) = 450.0 g
Molar mass of urea = 60 g/mole
Formula used :
![\Delta T_f=i\times K_f\times m\\\\T^o-T_s=i\times K_f\times\frac{\text{Mass of urea}\times 1000}{\text{Molar mass of urea}\times \text{Mass of X liquid}}](/tpl/images/0390/6513/41963.png)
where,
= change in freezing point
= freezing point of solution = ![-0.5^oC](/tpl/images/0390/6513/9fef8.png)
= freezing point of liquid X= ![0.4^oC](/tpl/images/0390/6513/86058.png)
i = Van't Hoff factor = 1 (for non-electrolyte)
= molal freezing point depression constant of X = ?
m = molality
Now put all the given values in this formula, we get
![[0.4-(-0.5)]^oC=1\times k_f\times \frac{5.90g\times 1000}{60g/mol\times 450.0g}](/tpl/images/0390/6513/c28e3.png)
![k_f=4.12^oC/m](/tpl/images/0390/6513/6d8e5.png)
Therefore, the molal freezing point depression constant of X is ![4.12^oC/m](/tpl/images/0390/6513/613fb.png)