What is the freezing point of an a nonionizing antifreeze solution containing 38.8g ethylene glycol, #C_2H_6O_2#, and 409 g of water?

Question

Henry Antrim · Accepted Answer

#T_"f sol" = -2.84^@"C"#

Your best bet for solving this issue is to use the freezing-point depression equation, which looks like this:

#DeltaT_f = i * K_f * b" "#, where

#DeltaT_f# - the freezing-point depression; #i# - the van't Hoff factor, equal to #1# for non-electrolytes; #K_f# - the cryoscopic constant of the solvent; #b# - the molality of the solution.

The cryoscopic constant of water is equal to #1.86 ""^@"C kg mol"^(-1)#

Tcriosebu.pdf https://tutor.hix.ai

You must first ascertain the molality of this solution, which is known to be the number of moles of solute divided by the mass of the solvent and expressed in kilograms! This will allow you to calculate the freezing point of the solution!

To calculate how many moles are in that sample, use the molar mass of ethylene glycol.

#38.8color(red)(cancel(color(black)("g"))) * ("1 mole C"_2"H"_6"O"_2)/(62.07color(red)(cancel(color(black)("g")))) = "0.625 moles C"_2"H"_6"O"_2#

This indicates that the solution's molality will be

#color(blue)(b = n/m)#

#b = "0.625 moles"/(409 * 10^(-3)"kg") = "1.528 molal"#

This indicates that this solution's freezing-point depression will be

#DeltaT_"f" = 1 * 1.86""^@"C" color(red)(cancel(color(black)("kg"))) color(red)(cancel(color(black)("mol"^(-1)))) * 1.528color(red)(cancel(color(black)("moles"))) color(red)(cancel(color(black)("kg"^(-1)))) = 2.84^@"C"#

The difference between the freezing points of the pure solvent and the solution is known as the freezing-point depression.

#color(blue)(DeltaT_"f" = T_"f"^@ - T_"f sol")#

This indicates that the solution's freezing point will be

#T_"f sol" = T_"f"^@ - DeltaT_"f"#

#T_"f sol" = 0^@"C" - 2.84^@"C" = color(green)(-2.84^@"C")#

Olivia Anton · Answer

undefined The freezing point of a nonionizing antifreeze solution containing 38.8 g of ethylene glycol (C2H6O2) and 409 g of water is approximately -9.5°C.