7. Colligative properties: tension depression, boiling point elevation, freezing point depression

description of the phenomena, laws, limitations, determination of the molecular weight

Description of the phenomena:

·       Ideal mixture:

o   there is interaction, but it is the same for different particles:

§  no matter what particle is present

§  their number is the decisive factor

§  thus for any property, the number of the particles is what matters

·       Laws of dilute solutions:

o   Freezing point depression

o   Boiling point elevation

o   Tension (=vapor pressure) depression

o   (osmotic pressure)

Freezing point depression

·       Generally the freezing point of the solution is lower that the freezing point of the solvent by itself

·       for a given amount of solvent, the freezing point depression only depends on the number of dissolved particles

·       Formula:
                       ΔT_F=ΔT_M*C_R
                 

o   ΔT_F: the temperature difference between the freezing point of the solution and the solvent

o   ΔT_M: constant for the solvent

o   C_R: Raoult concentration (molality) n_solute/m_solvent (in kg)
          

Molecular weight determination:
                        ΔT_F=ΔT_M*C_R
                       

·       ΔT_F: can be measured with a thermometer

·       ΔT_M: constant, it was determined before

·       C_R: can be expressed from the other two

·       from C_R we can determine both m_solute and n_solute by balancing the formula

·       from m_solute and n_solute we can determine the molecular weight M (m_solute/n_solute)

Limitations of the expression

·       the solute needs to be soluble

·       only pure solvent should freeze off (no solute) (eutectic phase diagram)

·       the solution has to be dilute enough (sufficiently dilute =5%, 0,1-0,2 molality → ,,thumb of rule”)

·       C_R is a measure of all solute particles. So, if for example NaCl is dissolved in water it dissolves into two mols of solute (Na⁺ and Cl^-) so in this case we must take dissociation into account (c→ van’t Hoff factor)

Boiling point elevation (tension depression)

·       Often the boiling point of a solution is higher than that of the pure solvent

·       for a given amount of solvent boiling point elevation only depends on the number of particles

·       Formula:

o   ΔT_B=ΔT_M*C_R

o   ΔT_B: the temperature difference between the boiling point of the solution and the solvent

o   ΔT_M: constant for the solvent

o   C_R: Raoult concentration (molality) n_solute/m_solvent (in kg)

·       Molecular weight determination

o   same way as with freezing point depression

Vapor pressure/tension depression:

·       the change in boiling point changes volatility which lowers the vapor pressure

·       Limitations:

o   solubility

o   only pure solvent evaporates, no solute (the vapor pressure of the solute is negligible)

o   the solution must be dilute enough (sufficiently dilute =5%, 0,1-0,2 molality → ,,thumb of rule”)

o   C_R is a measure of all solute particles. So, if for example NaCl is dissolved in water it dissolves into two mols of solute (Na⁺ and Cl^-) so in this case we must take dissociation into account (c→ van’t Hoff factor)

Problem

·       ΔT_M is small in most cases

·       the determination of bp and fp has to be very accurate (for dilute solutions sometimes thousandths degree centigrade)

·       particularly problematic for large M (molecular weight)