<u>Answer:</u> The molality of non-electrolyte is 24.69 m
<u>Explanation:</u>
We are given:
Mole fraction of saturated aqueous solution = 0.310
This means that 0.310 moles of non-electrolyte is present.
Moles of water (solvent) = 1 - 0.310 = 0.690 moles
To calculate the mass from given 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 water = 0.690 moles
Molar mass of water = 18 g/mol
Putting values in above equation, we get:
![0.690mol=\frac{\text{Mass of water}}{18g/mol}\\\\\text{Mass of water}=(0.690mol\times 18g/mol)=12.42g](https://tex.z-dn.net/?f=0.690mol%3D%5Cfrac%7B%5Ctext%7BMass%20of%20water%7D%7D%7B18g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20water%7D%3D%280.690mol%5Ctimes%2018g%2Fmol%29%3D12.42g)
To calculate the molality of solution, we use the equation:
![\text{Molality}=\frac{n_{solute}\times 1000}{W_{solvent}\text{ (in grams)}}](https://tex.z-dn.net/?f=%5Ctext%7BMolality%7D%3D%5Cfrac%7Bn_%7Bsolute%7D%5Ctimes%201000%7D%7BW_%7Bsolvent%7D%5Ctext%7B%20%28in%20grams%29%7D%7D)
Where,
= Moles of solute (non-electrolyte) = 0.310 moles
= Mass of solvent (water) = 12.42 g
Putting values in above equation, we get:
![\text{Molality of non-electrolyte}=\frac{0.310\times 1000}{12.42}\\\\\text{Molality of non-electrolyte}=24.96m](https://tex.z-dn.net/?f=%5Ctext%7BMolality%20of%20non-electrolyte%7D%3D%5Cfrac%7B0.310%5Ctimes%201000%7D%7B12.42%7D%5C%5C%5C%5C%5Ctext%7BMolality%20of%20non-electrolyte%7D%3D24.96m)
Hence, the molality of non-electrolyte is 24.69 m