Question

what is the minimum mass of ethylene glycol that must be dissolved in 14.5 kg of water to prevent the solution from freexing at -14.2

Answer 1

The minimum mass of ethylene glycol = 6.641 Kg

Step-by-step explanation:

`\Delta T_f= T_f-T_f'\\T_f'=T_f-\Delta T_f`

Where T_f = freezing point of pure solvent water, 0°C

T_f'= Freezing point of solvent after mixture

K_f = Freezing point depression constant = 1.86 °C/m

Moecular weight of ethylene glycol = 60 g/mol

Weight of ethylene glycol = 14.5 Kg= 14.5×10^3 g

molality of ethylene glycol

`m = (weight)/(mol.wt) *(1000)/(V)`

Substitute the values to calculate m

`m = (w)/(60) *(1000)/(14.5*1000)`

by formula

`0-(-14.2) =1.86(w)/(60) *(1000)/(14.5*1000)`

calculating we get w = 6641.93 g

Therefore, The minimum mass of ethylene glycol = 6.641 Kg