The question is incomplete, here is the complete question:
A 50 mL solution is initially 1.52% MgCl₂ by mass and has a density of 1.05 g/mL
What is the freezing point of the solution after you add an additional 1.37 g MgCl₂? (Use i = 2.5 for MgCl₂).
<u>Answer:</u> The freezing point of solution is -0.808°C
<u>Explanation:</u>
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 = 1.05 g/mL
Volume of solution = 50 mL
Putting values in above equation, we get:
![1.05g/mL=\frac{\text{Mass of solution}}{50mL}\\\\\text{Mass of solution}=(1.05g/mL\times 50mL)=52.5g](https://tex.z-dn.net/?f=1.05g%2FmL%3D%5Cfrac%7B%5Ctext%7BMass%20of%20solution%7D%7D%7B50mL%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20solution%7D%3D%281.05g%2FmL%5Ctimes%2050mL%29%3D52.5g)
We are given:
Percentage of magnesium chloride in the solution = 1.52 %
Mass of magnesium chloride in the solution = 1.52 % of 52.5 g = ![\frac{1.52}{100}\times 52.5=0.798g](https://tex.z-dn.net/?f=%5Cfrac%7B1.52%7D%7B100%7D%5Ctimes%2052.5%3D0.798g)
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 (water) = 0°C
i = Vant hoff factor = 2.5
= molal freezing point elevation constant = 1.86°C/m
= Given mass of solute (magnesium chloride) = [0.798 + 1.34] g = 2.138 g
= Molar mass of solute (magnesium chloride) = 95.2 g/mol
= Mass of solvent (water) = [52.5 - 0.798] g = 51.702 g
Putting values in above equation, we get:
![0-\text{Freezing point of solution}=1\times 1.86^oC/m\times \frac{2.138\times 1000}{95.2\times 51.702}\\\\\text{Freezing point of solution}=-0.808^oC](https://tex.z-dn.net/?f=0-%5Ctext%7BFreezing%20point%20of%20solution%7D%3D1%5Ctimes%201.86%5EoC%2Fm%5Ctimes%20%5Cfrac%7B2.138%5Ctimes%201000%7D%7B95.2%5Ctimes%2051.702%7D%5C%5C%5C%5C%5Ctext%7BFreezing%20point%20of%20solution%7D%3D-0.808%5EoC)
Hence, the freezing point of solution is -0.808°C