Answer:
1.86 m
Explanation:
Step 1: Calculate the mass of solute and solvent in 100 grams of solution
We have a 15.0% by mass solution of MgCl₂ (solute) in H₂O (water). In 100 g of solution, there are 15.0 g of solute and 100.0 g - 15.0 g = 85.0 g of solvent.
Step 2: Calculate the moles corresponding to 15.0 g of MgCl₂
The molar mass of MgCl₂ is 95.21 g/mol.
![15.0g \times \frac{1mol}{95.21 g} = 0.158mol](https://tex.z-dn.net/?f=15.0g%20%5Ctimes%20%5Cfrac%7B1mol%7D%7B95.21%20g%7D%20%3D%200.158mol)
Step 3: Convert the mass of water to kilograms
We will use the relationship 1 kg = 1,000 g.
![85.0g \times \frac{1kg}{1,000g} = 0.0850kg](https://tex.z-dn.net/?f=85.0g%20%5Ctimes%20%5Cfrac%7B1kg%7D%7B1%2C000g%7D%20%3D%200.0850kg)
Step 4: Calculate the molality of the solution
![m = \frac{0.158mol}{0.0850kg} = 1.86m](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B0.158mol%7D%7B0.0850kg%7D%20%3D%201.86m)