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A number of different methods may be employed for determination of molecular mass of any sample. But I want to limit our focus to the following methods,

  1. Relative lowering of partial pressure
  2. Elevation in Boiling point
  3. Depression in freezing point
  4. Osmotic pressure

All the methods rely on colligative properties of the sample and only work if the sample is non volatile. I want to know which method gives the most accurate value of molecular mass and if there is any explanation for that. Also are these methods more accurate than mass spectrometry?

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    $\begingroup$ Even ignoring mass spectroscopy, there is no fixed accuracy ordering of the four methods. Even for a substance that would be suitable for testing via all 4 methods, what are the various measurement errors in each method? The middle two obviously require accurate temperature measurements and the other two require accurate pressure measurements. Basically, this comes down to horses for courses. And mass spectroscopy, where applicable and available, will cross the finish line while those other nags are lumbering to the first turn. $\endgroup$
    – Ed V
    Commented Nov 13, 2021 at 2:07

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Osmotic pressure method is the most accurate and reliable method among the 4 colligative properties based molecular mass measurement methods.

Due to inverse relationship between the molar mass of solute and the measured colligative property, the highest difficulty is observed for the measurement of molar mass of high molecular weight species like polymers, proteins, etc.

The osmotic pressure is generally measured in terms of atmosphere or torr unit which is experimentally achieved by measuring the height of solution column in the capillary. As we know that 1 atm = 76 cm of Hg = 10.3 m of water column (Note: Density of water = 1 g/mL and density of Hg = 13.6 g/mL). Therefore for any solution we shall get appreciable column height, which can be measured accurately. Data for the same have been given below:

enter image description here

(Image Source: Manas Chanda, Introduction to Polymer Chemistry, A problem solving approach, 2nd Edition, CRC Press, Taylor & Francis, 2013.)

The experimental data comparing the 4 colligative properties based measurement methods have been given in the above table.

Therefore it is the experimental ease and accuracy of the measurement that makes the Osmotic pressure based molecular mass measurement method most suitable.

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