Question

Ethylene glycol, C2H6O2, is infinitely miscible (soluble) in water. It is a nonelectrolyte that is used as antifreeze. What is the lowest possible melting point for engine coolant that is 26.1% ethylene glycol

Answer 1

Answer: The lowest possible melting point for engine coolant that is 26.1% ethylene glycol is $-7.83^0C$

Explanation:

Depression in freezing point or melting point is given by:

$\Delta T_f=i\times K_f\times m$

$\Delta T_f=T_f^0-T_f=(0-T_f)^0C$ = Depression in freezing point

i= vant hoff factor  = ( 1 for non electrolyte)

$K_f$  = freezing point constant for water= $1.86^0C/m$

m= molality

$\Delta T_f=i\times K_f\times \frac{\text{mass of solute}}{\text{molar mass of solute}\times \text{weight of solvent in kg}}$

Given : 26.1 g of ethylene glycol in 100 g of water

Weight of solvent (water)= 100 g = 0.1 kg     (1kg=1000g)

Molar mass of solute (ethylene glycol)  = 62 g/mol

Mass of  solute (ethylene glycol) added = 26.1 g

$(0-T_f)^0C=1\times 1.86\times \frac{26.1g}{62g/mol\times 0.1kg}$

$(0-T_f)^0C=7.83$

$T_f=-7.83^0C$

Thus  the lowest possible melting point for engine coolant that is 26.1% ethylene glycol is $-7.83^0C$