What is the molality of #NaCl# if the freezing point of a #NaCl# solution is -5.58 C°?

Question

Cameron Andrews · Accepted Answer

#"1.50 mol kg"^(-1)#

The number of moles of solute per kilogram of solvent in a solution is indicated by its molality.

In this case, the only information you have is that a given sodium chloride solution has a freezing point of #-5.58^@"C"#.

As you are aware, a solution's freezing point is a colligative property, which means that it solely depends on the solute particle concentration.

Since sodium chloride is an electrolyte, it will entirely separate into sodium cations and chloride anions in an aqueous solution.

#"NaCl"_text((aq]) -> "Na"_text((aq])^(+) + "Cl"_text((aq])^(-)#

Observe that one mole of sodium chloride yields two moles of particles in solution: one mole of sodium cations and one mole of chloride anions.

This mans that sodium chloride has a van't Hoff factor, #i#, equal to #color(red)(2)#. The van't Hoff factor essentially tells you how many moles of particles you get per mole of solute dissolved in aqueous solution.

Now, you can compare the freezing point of the solution with that of pure water, which is equal to #0^@"C"#. The difference between the two freezing points will give you the freezing-point depression of the solution, #DeltaT_f#

#color(blue)(|bar(ul(color(white)(a/a)DeltaT_f = T_f^@ - T_"f sol"color(white)(a/a)|)))" "#, where

#T_f^@# - the freezing point of the pure solvent #T_"f sol"# - the freezing point of the solution

The freezing-point depression in your situation will be equal to

#DeltaT_f = 0^@"C" - (-5.58^@"C") = 5.58^@"C"#

The molality of the solution has an impact on the freezing-point depression as well.

#color(blue)(|bar(ul(color(white)(a/a)DeltaT_f = i * K_f * bcolor(white)(a/a)|)))" "#, where

#DeltaT_f# - the freezing-point depression; #i# - the van't Hoff factor #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

Rearrange the above equation to solve for #b#

#DeltaT_f = i * K_f * b implies b = (DeltaT_f)/(i * K_f)#

Enter your values to obtain

#b = (5.58color(red)(cancel(color(black)(""^@"C"))))/(color(red)(2) * 1.86color(red)(cancel(color(black)(""^@"C"))) "kg mol"^(-1)) = color(green)(|bar(ul(color(white)(a/a)"1.50 mol kg"^(-1)color(white)(a/a)|)))#

Three sig figs are used to round the result.

Xavier Avery · Answer

undefined To determine molality, additional information such as the freezing point depression constant (Kf) of the solvent is required. Without that, molality cannot be calculated.