Answer : The mass of KNO₃ added must be, ![1.08\times 10^2g](https://tex.z-dn.net/?f=1.08%5Ctimes%2010%5E2g)
Explanation : Given,
Molal-freezing-point-depression constant
for water = ![1.86^oC/m](https://tex.z-dn.net/?f=1.86%5EoC%2Fm)
Volume of water = 275 mL
Molar mass of KNO₃ = 101.1 g/mole
First we have to calculate the mass of water.
![\text{Mass of water}=\text{Density of water}\times \text{Volume of water}](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20water%7D%3D%5Ctext%7BDensity%20of%20water%7D%5Ctimes%20%5Ctext%7BVolume%20of%20water%7D)
Density of water = 1.00 g/mL
![\text{Mass of water}=1.00g/mL\times 275mL=275g=0.275kg](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20water%7D%3D1.00g%2FmL%5Ctimes%20275mL%3D275g%3D0.275kg)
Now we have to calculate the mass of KNO₃
Formula used :
![\Delta T_f=i\times K_f\times m\\\\T^o-T_s=i\times K_f\times\frac{\text{Mass of }KNO_3}{\text{Molar mass of }KNO_3\times \text{Mass of water in Kg}}](https://tex.z-dn.net/?f=%5CDelta%20T_f%3Di%5Ctimes%20K_f%5Ctimes%20m%5C%5C%5C%5CT%5Eo-T_s%3Di%5Ctimes%20K_f%5Ctimes%5Cfrac%7B%5Ctext%7BMass%20of%20%7DKNO_3%7D%7B%5Ctext%7BMolar%20mass%20of%20%7DKNO_3%5Ctimes%20%5Ctext%7BMass%20of%20water%20in%20Kg%7D%7D)
where,
= change in freezing point
= freezing point of solution = ![-14.5^oC](https://tex.z-dn.net/?f=-14.5%5EoC)
= freezing point of water = ![0.0^oC](https://tex.z-dn.net/?f=0.0%5EoC)
i = Van't Hoff factor = 2 (for KNO₃ electrolyte)
= freezing point constant for water = ![1.86^oC/m](https://tex.z-dn.net/?f=1.86%5EoC%2Fm)
m = molality
Now put all the given values in this formula, we get
![0.0^oC-(-14.5^oC)=2\times (1.86^oC/m)\times \frac{\text{Mass of }KNO_3}{101.1g/mol\times 0.275kg}](https://tex.z-dn.net/?f=0.0%5EoC-%28-14.5%5EoC%29%3D2%5Ctimes%20%281.86%5EoC%2Fm%29%5Ctimes%20%5Cfrac%7B%5Ctext%7BMass%20of%20%7DKNO_3%7D%7B101.1g%2Fmol%5Ctimes%200.275kg%7D)
![\text{Mass of }KNO_3=108.369g=1.08\times 10^2g](https://tex.z-dn.net/?f=%5Ctext%7BMass%20of%20%7DKNO_3%3D108.369g%3D1.08%5Ctimes%2010%5E2g)
Therefore, the mass of KNO₃ added must be, ![1.08\times 10^2g](https://tex.z-dn.net/?f=1.08%5Ctimes%2010%5E2g)