Colligative Properties Chem Experiment!?

Question

Hi everyone, I REALLY need ur help. There's a question seems like I can't quite understand (I have some idea about it though): the digital thermometer is miscalibrated by 0.15C higher over its entire range, how will the reported moles of solute in solution be affected? I'm doing a lab determining molar mass of a solid. And in the experiment, I have to use the thermometer to record the temperature while observing and then plot the points on the graph to determine the freezing point. I'm looking for a serious answer! Please help me! Thank you

Answer 1

I assume (for simplicity) that the compound in question is not an electrolyte. Then

ΔTf = Kf*1000*g/(MW*G)

where
Kf the cryoscopic constant of the solvent
g the grams of solute
MW the molecular weight of the solute
G the grams of solvent.

In order to find the MW, you need to find the ΔTf for different grams of solute, do a plot, fit the data to a linear equation and from the slope, that will be equal to Kf*1000/(G*MW) you calculate MW. As far as I know that's why you do the graph-not for determining the freezing point.

If you measured the freezing point of pure solvent with the same thermometer, then the error is the same for both measurements (pure solvent and solution) so the difference ΔTf will be correct.
In detail: if Tfo is the true freezing point of pure solvent, Tf of the solution, Tfo' whatyou measure with the thermometer for the solvent and Tf' for the solution then you have
Tfo'=Tfo+0.15
Tf' =Tf+0.15
so Tfo'-Tf'= (Tfo+0.15) - (Tf+0.15) = Tfo-Tf =>
ΔTf'=ΔTf

If you use Tfo from the literature, then
ΔTf' = Tfo-Tf'= Tfo -(Tf+0.15) =ΔTf-0.15
This means that you'll find a smaller depression in the freezing point than you should (since Tfo>Tf thus ΔTf>0). Since MW and ΔTf are inversely proportional you will calculate a higher MW value than the true.

(Edit) I forgot to say about the moles of solute.
ΔTf = Kf*m
where m = molality = moles of solute per kg of solvent.
So since ΔTf and m are directly proportional, finding a smaller ΔTf means that you find fewer moles solute than you should.