Question #4f3c7

1 Answer
Jul 9, 2017

Answer:

WARNING! Long answer! You must add 3.86 L of ethylene glycol. The boiling point of the mixture will be 105.23 °C.

Explanation:

(a) Volume of antifreeze

The formula for freezing point depression #ΔT_"f"# is

#color(blue)(bar(ul(|color(white)(a/a)ΔT_"f" = K_"f"bcolor(white)(a/a)|)))" "#

where

#K_"f"# = the molal freezing point depression constant of the solvent
#b# = the molality of the solution

We can rearrange the formula to get

#b = (ΔT_"f")/K_"f"#

In your problem,

#ΔT_"f" = "19.0 °C"#
#K_"f" = "1.86 °C·kg·mol"^"-1"#

#b = (19.0 color(red)(cancel(color(black)("°C"))))/(1.86 color(red)(cancel(color(black)("°C")))·"kg·mol"^"-1") = "10.22 mol·kg"^"-1"#

#"Mass of water" = 6750 color(red)(cancel(color(black)("mL water"))) × "1.00 g water"/(1 color(red)(cancel(color(black)("mL water")))) = "6750 g water" = "6.75 kg water"#

#"Amount of EG" = 6.75 color(red)(cancel(color(black)("kg water"))) × "10.22 mol EG"/(1 color(red)(cancel(color(black)("kg water")))) = "68.95 mol EG"#

#"Mass of EG" = 68.95 color(red)(cancel(color(black)("mol EG"))) × "62.07 g EG"/(1 color(red)(cancel(color(black)("mol EG")))) = "4280 g EG"#

#"Volume of EG" = 4280 color(red)(cancel(color(black)("g EG"))) × "1 mL EG"/(1.11 color(red)(cancel(color(black)("g EG")))) = "3860 mL EG" = "3.86 L EG"#

You must add 3.86 L of ethylene glycol to the radiator.

(b)) Boiling point of solution

The formula for boiling point elevation #ΔT_"b"# is

#color(blue)(bar(ul(|color(white)(a/a)ΔT_"b" = K_"b"bcolor(white)(a/a)|)))" "#

where

#K_"b"# = the molal boiling point elevation constant of the solvent (#"0.512 °C·kg·mol"^"-1"#).

We can combine the boiling point and freezing point formulas to get

#(ΔT_text(b))/(ΔT_text(f)) = (K_"b"color(red)(cancel(color(black)(b))))/(K_text(f)color(red)(cancel(color(black)(b)))) = (K_"b")/(K_text(f))#

We can rearrange this equation to get

#ΔT_text(b) = ΔT_text(f) × K_text(b)/K_text(f) = "19.0 °C" × (0.512 color(red)(cancel(color(black)("°C·kg·mol"^"-1"))))/(1.86 color(red)(cancel(color(black)("°C·kg·mol"^"-1")))) = "5.23 °C"#

#T_text(b) = "100 °C + 5.23 °C = 105.23 °C"#