Answer : The molality of solution is, 0.866 mole/kg
Explanation :
The relation between the molarity, molality and the density of the solution is,
![d=M[\frac{1}{m}+\frac{M_b}{1000}]](https://tex.z-dn.net/?f=d%3DM%5B%5Cfrac%7B1%7D%7Bm%7D%2B%5Cfrac%7BM_b%7D%7B1000%7D%5D)
where,
d = density of solution = 1.0052 g/ml
m = molality of solution = ?
M = molarity of solution = 0.828 M = 0.828 mol/L
= molar mass of solute (acetic acid) = 60.05 g/mole
Now put all the given values in the above formula, we get the molality of the solution.
![1.0052g/ml=0.828mol/L\times [\frac{1}{m}+\frac{60.05g/mole}{1000}]](https://tex.z-dn.net/?f=1.0052g%2Fml%3D0.828mol%2FL%5Ctimes%20%5B%5Cfrac%7B1%7D%7Bm%7D%2B%5Cfrac%7B60.05g%2Fmole%7D%7B1000%7D%5D)
![m=0.866mol/kg](https://tex.z-dn.net/?f=m%3D0.866mol%2Fkg)
Therefore, the molality of solution is, 0.866 mole/kg