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)
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