Question

The value of ${ K }_{ f }$ of water is ${ 1.86K\quad kg mol }^{ -1 }$. If ${ 1 }$ kg of water is filled in your automobile radiation then how much gm of ethylene glycol will be added to decrease the freezing point of the solution to ${ -2.8 }^{ \circ }{ C }$.

Answer 1

Hint: Freezing point:- The temperature at which liquid turns into a solid when cooled is called a freezing point of that particular matter.

Complete answer:
Depression in freezing point:- When we add a non-volatile solid, in the pure liquid, the freezing point of the liquid is lowered, as the vapour pressure of the liquid is lowered, due to the presence of non-volatile solute particles at the surface of the liquid.
It is given that,
Let ${ W }_{ A }$ be the mass of ethylene glycol needed to be added to the automobile radiation.
Mass of the solvent (water) = ${ W }_{ A }= { 1 }kg = { 1000g }$
${ K }_{ f }$ of water = ${ 1.86K\quad kg mol }^{ -1 }$.
Freezing point of water, ${ T }_{ f }= { 0 }^{ \circ }{ C }$
Freezing point of solution = ${ -2.8 }^{ \circ }{ C }$
Mass of the solute, ${ M }_{ B }= { 62 }g/mol$
Now, use the formula;
$\Delta { T }_{ f }{ =T }_{ f }{ -T }_{ s }{ =1000\times K }_{ f }{ \times W }_{ B }\div { W }_{ A }{ \times M }_{ B }$

${ W }_{ B }{ =(T }_{ f }{ -T }_{ s }{ )\times W }_{ A }{ \times M }_{ B }{ \div 1000\times K }_{ f }$
= ${ \{ 0-(-2.8)\} \times 1000\times 62\div 1000\times 1.86 }$
= ${ 280\div 3 }$
= ${ 93.33g }$
Therefore, the mass of ethylene glycol added, ${ W }_{ B }= { 93.33g }$.

Additional Information:
Adding a solute to a solvent decreases the temperature at which the liquid solvent becomes a solid.
At the freezing point, the vapour pressure of both the solid and liquid form of a compound must be equal.
It is a colligative property.

Note: The possibility to make a mistake is that there is a difference between the freezing point and freezing point depression. Freezing point is the temperature at which liquid turns into a solid when cooled is called a freezing point of that particular matter while freezing point depression is the difference in the freezing points of the solution.