Freezing Point Depression:

The freezing point of a pure solution is depressed (lowered) when a non volatile solute is added. The extent of the change is related to the amount of solute present by the following equation.

    (eqn 1)

where

T is the difference between freezing point of the pure solvent and thefreezing point of the solution after the solute has been added.
Kf is the molal freezing point depression constant
m is the molality of the solution. Kf, the molal freezing point depression constant, can be readily calculated from eqn 2 and the freezing point of pure t-butanol solvent.

    (eqn 2)

where

R is the gas constant. use the value 1.987 cal/mol K
Tf is the freezing point of the pure t-butanol solvent expressed in Kelvins. (°C + 273.15)
is a constant. For t-butanol this constant has a value of 21.88 cal/g

The units for Kf are K kg/mol. There is no uncertainty analysis for Kf.

Molecular Weight of the Uknown Acid:

The molality is defined as

    (eqn 3)

and in this experiment the unknown acid is the solute. Substituting eqn 3 into eqn 1 we get

    (eqn 4)

and since we weighted the solvent in grams, eqn 4 becomes

    (eqn 5)

We can express the moles Unk. Acid as

    (eqn 6)

and substitution of eqn 6 into eqn 5 gives

     (eqn 7)

We can calculate the Mol. Wt of the Unk. Acid by rearranging eqn 7 to give

    (eqn 8)

Uncertainty Analysis:

For the uncertainty analysis, we only need to consider the uncertainty in the beam balance and thermometer. Therefore T = ± 0.1 ° and wt. solvent = ± 0.10g. The upper limit (UL) and lower limit (LL) can be calculated by

    (eqn 9)

     (eqn 10)