Boiling point elevation Clausius-Clapeyron equation

Raoult s law works for small polymers as well as small molecules. Determination of M is based for both ebulliometry (boiling point elevation) and cryometry (freezing point lowering) on the Clausius-Clapeyron equation ... 

Since we know how the solution vapor pressure varies with concentration (the relationship being given by Equation 6.5-2) and temperature (through the Clausius-Clapeyron equation. Equation 6.1-3), we can determine the relationships between concentration and both boiling point elevation and freezing point depression. The relationships are particularly simple for dilute solutions x — 0, where x is solute mole fraction). 

An expression for the boiling point elevation may readily be derived using the Clausius-Clapeyron equation (see Box 2.1). This expression allows the calculation of the increase of boiling point, AT, from the molality, m, of the solution using... 

The temperature of the adsorbent and vapor with which it is in equilibrium must remain constant during the measurement. With nitrogen as the adsorbate the coolant most often used is liquid nitrogen. The temperature of liquid nitrogen is dependent on ambient pressure and the presence of impurities in the liquid which tend to elevate the boiling point. The Clapeyron-Clausius equation can be used to calculate the change... 

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