What is the molality of $ {C_2}{H_5}OH $ in water solution which will freeze at $ - 10 \circ C $ [Mol wt of $ {C_2}{H_5}OH = 46 $ , $ {K_f} $ for water $ 1.86Kkgmo{l^{ - 1}} $
a) $ 6.315m $
b) $ 63.15m $
c) $ 3.540m $
d) $ 5.3m $

Hint: The molecular formula of ethanol is $ {C_2}{H_5}OH $ .It’s a flammable, colorless liquid with a boiling point of $ 78.5^\circ {\text{ }}C $ . Since we need to find molality we need to use a formula which will give us a relation between Depression of freezing point,Depression constant and molality.

Complete answer:
The freezing point of a solution is always lower than pure solvent.This phenomenon can be explained by the hypothesis that when a substance starts to freeze, the molecules start losing their internal energy and begin to slow down due to the decrease in temperature, and the intermolecular forces start to take over the molecules. The molecules will then arrange themselves in a set pattern, and thus turn into a solid. For example, as water is cooled to the freezing point, its molecules become slower and hydrogen bonds begin to “stick” more, eventually creating a solid.The solvent will also experience an elevation in boiling point when solute is added.
We know that,
Depression in freezing point = Depression Constant × Molality
 $ \vartriangle T = {K_f} \times m $
Here it has been provided in the question that, $ \vartriangle T = 10 \circ C $ , $ {K_f} = 1.86 $ and let molality of the solution be $ x $ hence,
 $ 10 = 1.86 \times x $
Taking constant on one side,
 $ \dfrac{{10}}{{1.86}} = x $
Solving this we get,
 $ x = 5.33m $
By comparing our answer with the given options we conclude that the correct option is option D) 5.3m.

Note:
Ethanol has a very wide range of industrial applications.It’s often used as a fuel additive and some commercially available fuels contain upto $ 25\% $ ethanol.It often forms the base of alcohol based hand sanitizers. Ethanol is used industrially in the production of ethyl esters, acetic acid, diethyl ether, and ethyl amines.