Answer : The molality of the solution is 0.692m. The mole fraction of water is 0.988.
Explanation :
Molality :
The molality of a solution is calculated as,
![molality = \frac{mol (solute)}{kg (solvent)}](https://tex.z-dn.net/?f=molality%20%3D%20%5Cfrac%7Bmol%20%28solute%29%7D%7Bkg%20%28solvent%29%7D)
Step 1 : Find moles of Potassium Nitrate KNO₃.
![mol = \frac{Grams KNO_{3}}{Molar Mass}](https://tex.z-dn.net/?f=mol%20%3D%20%5Cfrac%7BGrams%20KNO_%7B3%7D%7D%7BMolar%20Mass%7D)
Molar mass of KNO₃ is 101.1 g/mol
Mass of KNO₃ is 3.50 g
![mol KNO_{3} = \frac{3.50g}{101.1g/mol} = 0.0346](https://tex.z-dn.net/?f=mol%20KNO_%7B3%7D%20%3D%20%5Cfrac%7B3.50g%7D%7B101.1g%2Fmol%7D%20%3D%200.0346)
Step 2 : Find kg of the solvent
Water is solvent here.
Mass of water = 50.0 g = 0.050 kg
Step 3 : Use molality formula
Let us use these values to find molality of the solution.
![molality = \frac{0.0346mol}{0.050kg} = 0.692 m](https://tex.z-dn.net/?f=molality%20%3D%20%5Cfrac%7B0.0346mol%7D%7B0.050kg%7D%20%3D%200.692%20m)
The molality of the solution is 0.692 m
Mole fraction :
The mole fraction of a component of a mixture is calculated as,
![X_{A} = \frac{molA}{Total Moles}](https://tex.z-dn.net/?f=X_%7BA%7D%20%3D%20%5Cfrac%7BmolA%7D%7BTotal%20Moles%7D)
Step 1 : Find moles of water
Let us find moles of water using the mole formula
Molar mass of water is 18.02 g/mol
![mol H_{2}O = \frac{50.0 g H_{2}O}{18.02 g/mol} = 2.775](https://tex.z-dn.net/?f=mol%20H_%7B2%7DO%20%3D%20%5Cfrac%7B50.0%20g%20H_%7B2%7DO%7D%7B18.02%20g%2Fmol%7D%20%3D%202.775)
Step 2 : Use mole fraction formula
Mole fraction of H₂O = ![X_{H_{2}O} = \frac{mol H_{2}O}{(mol KNO_{3} + mol H_{2}O)}](https://tex.z-dn.net/?f=X_%7BH_%7B2%7DO%7D%20%3D%20%5Cfrac%7Bmol%20H_%7B2%7DO%7D%7B%28mol%20KNO_%7B3%7D%20%2B%20mol%20H_%7B2%7DO%29%7D)
![X_{H_{2}O} = \frac{2.775}{(0.0346 + 2.775)} = \frac{0.0346}{2.8096} = 0.988](https://tex.z-dn.net/?f=X_%7BH_%7B2%7DO%7D%20%3D%20%5Cfrac%7B2.775%7D%7B%280.0346%20%2B%202.775%29%7D%20%3D%20%5Cfrac%7B0.0346%7D%7B2.8096%7D%20%3D%200.988)
Mole fraction of H₂O is 0.988