1.32g of unknown nonelectrolyte is dissolved in 428g of cyclohexane, lowering freezing point from 6.50 degree Celsius to 3.91 degree Celsius. The molal freez point constant of cyclohexane=20.2 degree Celsius/m. What is molar mass of unknown nonelectrolyt?

#M_m = "24.1 g/mol"#

Freezing point depression is given by:

#DeltaT_f = T_f - T_f^"*" = -iK_fm#,

where:

• #T_f# is the freezing point of the solution. #"*"# indicates pure solvent.
• #i# is the van't Hoff factor, i.e. the number of dissociated solute particles per undissociated solute particle.
• #K_f# is the freezing point depression constant of the solvent.
• #m# is the molality of the solution, i.e. #"mol solute/kg solvent"#.

We want the molar mass, and the first thing we can find is the molality.

#m = (DeltaT_f)/(-iK_f)#

We have that #i = 1# for nonelectrolytes (dissolves with zero dissociation), and #K_f = 20.2^@ "C/kg"cdot"mol"#.

Therefore, the molality is:

#m = (3.91 - 6.50^@ "C")/(-(1)(20.2^@ "C"cdot"kg/mol"))#

#=# #"0.128 mol solute/kg solvent"#

There are #"428 g"# of cyclohexane solvent, so there are

#"0.128 mol solute"/cancel"kg solvent" xx 0.428 cancel"kg solvent"#

#=# #ul"0.0549 mols solute"# dissolved in it.

As a result, knowing that we dissolved #"1.32 g"# of the solute, the molar mass is:

#color(blue)(M_m) = "1.32 g solute"/"0.0549 mol solute" = color(blue)ul("24.1 g/mol")#