Question

What mass of ethylene glycol (Molar mass $ = 62.0{\text{ }}g{\text{ }}mo{l^{ - 1}}$ ) must be added to $5.50kg$ of water to lower the freezing point of water from ${0^0}C$ to $ - {10^0}C$ ? (${K_f}$ for water $ = 1.86{\text{ }}K{\text{ }}Kg{\text{ }}mo{l^{ - 1}}$ )

Answer 1

Hint- In order to deal with this question first we will write the definition of molecular mass of compound further we will write all the given data and by using the relation between mass of solution, mass of solute and temperature difference we will get the required answer.

Complete step-by-step answer:
Molecular mass: The mass of a given molecule is the molecular mass (m): it is expressed in daltons (Da or u). Similar molecules of the same compound may have different molecular masses, because they contain different element isotopes. The related sum of relative molecular mass, as described by IUPAC, is the ratio of a molecule's mass to the single unit of atomic mass (also known as the dalton) and is unitless.

Given that:
Molar mass of ethylene glycol ${M_B} = 62.0{\text{ }}g{\text{ }}mo{l^{ - 1}}$
Weight of water ${W_A} = 5.50kg = 5500gm$
${K_f} = 1.86{\text{ }}K{\text{ }}Kg{\text{ }}mo{l^{ - 1}}$
$
  \Delta {T_f} = {0^0}C - \left( { - {{10}^0}C} \right) \\
  \Delta {T_f} = \left( {0 + 273} \right)K - \left( { - 10 + 273} \right)K \\
  \Delta {T_f} = 10K \\
 $
As we know that relation between temperature difference and molecular mass of compound is given as:
$\Delta {T_f} = {K_f} \times \dfrac{{{W_B}}}{{{M_B}}} \times \dfrac{{1000}}{{{W_A}}}$
Substitute all the values in above formula we get:
$
   \Rightarrow 10 = 1.86 \times \dfrac{{{W_B}}}{{62}} \times \dfrac{{1000}}{{5500}} \\
   \Rightarrow {W_B} = \dfrac{{62 \times 5500 \times 10}}{{1000 \times 1.86}} \\
   \Rightarrow {W_B} = \dfrac{{3410000}}{{1860}} \\
   \Rightarrow {W_B} = 1833.3g \\
 $
Hence the mass of ethylene glycol to be added is $1833.3g$

Note- Ethylene glycol is a colorless, odorless, bittersweet-tasting solvent that has various industrial and household applications. Ethylene glycol is a "toxic alcohol," which means that although it is chemically similar to ethanol (the main ingredient in alcoholic beverages); it is much more harmful when drunk.
Ethylene glycol is a chemical that is widely used in various consumer and industrial uses including antifreeze and refrigerants. Ethylene glycol helps avoid the freezing of the car's engine in winter, and serves as a coolant to minimize overheating in summer.