Respuesta :
Explanation:
As it is assumed that we are given 100 g of solution.
Therefore, mass of ethylene glycol is as follows.
          [tex]\frac{21.7}{100} \times 100[/tex]
            = 21.7 g
Now, number of moles of ethylene glycol is calculated as follows.
   No. moles of ethylene glycol = [tex]\frac{mass}{\text{molar mass}}[/tex]
                            = [tex]\frac{21.7 g}{62.07 g/mol}[/tex]                 Â
                            = 0.349 mol
Hence, mass of water = (100 - 21.7) g = 78.3 g
                   = 0.783 kg       (a 1 kg = 100 g)
As, molality is number of moles present in kg of solvent.
So, Â Â Â Â Â Molality = [tex]\frac{\text{no. of moles of ethylene glycol}}{\text{mass of water in kg}}[/tex]
               = [tex]\frac{0.349 mol}{0.783}[/tex]
               = 0.445 m
Melting point depression ([tex]\Delta T_{f}[/tex]) = [tex]K_{f} \times molality[/tex]
                       = [tex]1.86 ^{o}C/m \times 0.445 m[/tex]
                       = [tex]0.828^{o}C[/tex]
Therefore, melting point of solution will be calculated as follows.
       Melting point of solution = Melting point of water - [tex]\Delta T_{f}[/tex]
                            = [tex](0.00 - 0.828)^{o}C[/tex]
                            = [tex]-0.828^{o}C[/tex]
Thus, we can conclude that the lowest possible melting point for given engine coolant is [tex]-0.828^{o}C[/tex].
