<u>Answer:</u> The freezing point of solution is -0.974°C
<u>Explanation:</u>
- To calculate the concentration of solute, we use the equation for osmotic pressure, which is:
![\pi=iMRT](https://tex.z-dn.net/?f=%5Cpi%3DiMRT)
where,
= osmotic pressure of the solution = 12.1 atm
i = Van't hoff factor = 1 (for non-electrolytes)
M = molarity of solute = ?
R = Gas constant = ![0.0821\text{ L atm }mol^{-1}K^{-1}](https://tex.z-dn.net/?f=0.0821%5Ctext%7B%20L%20atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D)
T = temperature of the solution = 298 K
Putting values in above equation, we get:
![12.1atm=1\times M\times 0.0821\text{ L.atm }mol^{-1}K^{-1}\times 298K\\\\M=\frac{12.1}{1\times 0.0821\times 298}=0.495M](https://tex.z-dn.net/?f=12.1atm%3D1%5Ctimes%20M%5Ctimes%200.0821%5Ctext%7B%20L.atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20298K%5C%5C%5C%5CM%3D%5Cfrac%7B12.1%7D%7B1%5Ctimes%200.0821%5Ctimes%20298%7D%3D0.495M)
This means that 0.495 moles of glucose is present in 1 L or 1000 mL of solution
- To calculate the mass of solution, we use the equation:
![\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}](https://tex.z-dn.net/?f=%5Ctext%7BDensity%20of%20substance%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20substance%7D%7D%7B%5Ctext%7BVolume%20of%20substance%7D%7D)
Density of solution = 1.034 g/mL
Volume of solution = 1000 mL
Putting values in above equation, we get:
![1.034g/mL=\frac{\text{Mass of solution}}{1000mL}\\\\\text{Mass of solution}=(1.034g/mL\times 1000mL)=1034g](https://tex.z-dn.net/?f=1.034g%2FmL%3D%5Cfrac%7B%5Ctext%7BMass%20of%20solution%7D%7D%7B1000mL%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20solution%7D%3D%281.034g%2FmL%5Ctimes%201000mL%29%3D1034g)
- To calculate the number of moles, we use the equation:
![\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20moles%7D%3D%5Cfrac%7B%5Ctext%7BGiven%20mass%7D%7D%7B%5Ctext%7BMolar%20mass%7D%7D)
Moles of glucose = 0.495 moles
Molar mass of glucose = 180.16 g/mol
Putting values in above equation, we get:
![0.495mol=\frac{\text{Mass of glucose}}{180.16g/mol}\\\\\text{Mass of glucose}=(0.495mol\times 180.16g/mol)=89.18g](https://tex.z-dn.net/?f=0.495mol%3D%5Cfrac%7B%5Ctext%7BMass%20of%20glucose%7D%7D%7B180.16g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20glucose%7D%3D%280.495mol%5Ctimes%20180.16g%2Fmol%29%3D89.18g)
Depression in freezing point is defined as the difference in the freezing point of pure solution and freezing point of solution.
- The equation used to calculate depression in freezing point follows:
![\Delta T_f=\text{Freezing point of pure solution}-\text{Freezing point of solution}](https://tex.z-dn.net/?f=%5CDelta%20T_f%3D%5Ctext%7BFreezing%20point%20of%20pure%20solution%7D-%5Ctext%7BFreezing%20point%20of%20solution%7D)
To calculate the depression in freezing point, we use the equation:
![\Delta T_f=iK_fm](https://tex.z-dn.net/?f=%5CDelta%20T_f%3DiK_fm)
Or,
![\text{Freezing point of pure solution}-\text{Freezing point of solution}=i\times K_f\times \frac{m_{solute}\times 1000}{M_{solute}\times W_{solvent}\text{ (in grams)}}](https://tex.z-dn.net/?f=%5Ctext%7BFreezing%20point%20of%20pure%20solution%7D-%5Ctext%7BFreezing%20point%20of%20solution%7D%3Di%5Ctimes%20K_f%5Ctimes%20%5Cfrac%7Bm_%7Bsolute%7D%5Ctimes%201000%7D%7BM_%7Bsolute%7D%5Ctimes%20W_%7Bsolvent%7D%5Ctext%7B%20%28in%20grams%29%7D%7D)
where,
Freezing point of pure solution = 0°C
i = Vant hoff factor = 1 (For non-electrolytes)
= molal freezing point elevation constant = 1.86°C/m
= Given mass of solute (glucose) = 89.18 g
= Molar mass of solute (glucose) = 180.16 g/mol
= Mass of solvent (water) = [1034 - 89.18] g = 944.82 g
Putting values in above equation, we get:
![0-\text{Freezing point of solution}=1\times 1.86^oC/m\times \frac{89.18\times 1000}{180.16g/mol\times 944.82}\\\\\text{Freezing point of solution}=-0.974^oC](https://tex.z-dn.net/?f=0-%5Ctext%7BFreezing%20point%20of%20solution%7D%3D1%5Ctimes%201.86%5EoC%2Fm%5Ctimes%20%5Cfrac%7B89.18%5Ctimes%201000%7D%7B180.16g%2Fmol%5Ctimes%20944.82%7D%5C%5C%5C%5C%5Ctext%7BFreezing%20point%20of%20solution%7D%3D-0.974%5EoC)
Hence, the freezing point of solution is -0.974°C