Question

Calculate the amount of ice that will separate out on cooling a solution containing $50$ g of ethylene glycol in $200$g of water to $-9.3°C$.

Molal depression constant for water is $1.86$ K kg/mol

• A. $8.80$g
• B. $6$g
• C. $7.50$g
• D. $8.91$g

Answer 1

The correct option is D $8.91$g

Molal depression constant = Depression in Kelvin per mole of solute present in kg of solvent.

molecular mass of Ethylene Glycol = $C_2{H}_6{O}_2$ = 62 gm/mole

Number of moles/kg of water = $50/62\ast 1000/200$ = $4$ moles/kg

Actual depression in freezing point temperature: $1.86°K\ast 4$ = $7.44°K$

Specific heat of Ice = $2J/gm-°K$

The heat released from $200$gm of water(ice) due to the lowering of temperature

$=7.44\ast 2\ast 200=2,976J$

Latent heat of fusion of ice = $334kJ/kg=334J/gm$

Amount of ice that will melt away due to availability of $2,976J$:

= $2,976/334$

= $8.91$ gm