The liquid used in automobile cooling systems is prepared by

The liquid used in automobile cooling systems is prepared by dissolving ethylene glycol (HOCH2CH2OH) in water. Ethylene glycol has a molar mass of 62.07 g/mol and a density of 1.115 g/mL at 50.0°C. Calculate the vapor pressure at 50°C of a coolant solution that is 59.0:41.0 ethylene glycol-to-water by volume. At 50.0°C, the density of water is 0.9880 g/mL, and its vapor pressure is 92 torr. The vapor pressure of ethylene glycol is less than 1 torr at 50.0°C

Solution

he vapour pressure will be the sum of partial pressures of both the components.

Partial pressure = mole fraction × pure vapour pressure

Let us assume the solution volume be 100 ml

So the volume of ethylene glycol will be 56 ml

Density = mass / volume

So mass of glycol = 1.115 × 56 = 62.44 grams

Number of moles = 62.44 / 62.07 = 1.005 moles

Likewise volume of water = 44 ml

And mass = 44× 0.9880 = 43.472 grams

Number of moles of water = 43.472/ 18.016 = 2.412 moles

Mole fraction of glycol = 1.005 / (1.005+2.412) = 0.294

Mole fraction of water = 1 - 0.294 = 0.706

Partial pressure of glycol = 1 × 0.294 = 0.294 torr

Partial pressure of water = 92 × 0.706 = 64.95 torr

Total vapour pressure = 0.312 + 64.95 = 65.24 torr

So the vapour pressure of the coolant will be 65.24 torr