Advertisement Remove all ads

Advertisement Remove all ads

Advertisement Remove all ads

Answer in Brief

Derivation

Derive van’t Hoff general solution equation

Derive van’t Hoff general solution equation for ‘n’ moles of solute.

Advertisement Remove all ads

#### Solution

- According to van't Hoff-Boyle's law, osmotic pressure of a dilute solution is inversely proportional to the volume containing 1 mole of solute at constant temperature and according to van't Hoff-Charles' law, osmotic pressure of a dilute solution is directly proportional to the absolute temperature, at constant concentration.
- If π is the osmotic pressure, V is the volume of the solution and T is the absolute temperature, then

π ∝ `1/"V"` ...(1) ...[ van't Hoff-Boyle's law at constant temperature]

∴ πV = constant

π ∝ T .....(2) ...[ van't Hoff-Charles' law at constant concentration ]

∴ `π/"T"` = constant - Combining (1) and (2) we get,

π ∝ `"T"/"V"`

∴ π = Constant x `"T"/"V"`

∴ πV = R'T, where R' is a constant. - This equation is parallel to the ideal gas equation PV = RT ( n = 1 )

Since, the calculated value of R' is almost same as R, the equation can be written as πV = RT ( for 1 mole of solute ) - This equation was derived for 1 mole of solute dissolved in V dm
^{3}. If n moles of solute are dissolved in V dm^{3 }of solution, the equation becomes

πV = nRT

∴ π = ` "nRT"/"V"` - C = `"n"/"V"`

∴ π = CRT

where,

π = osmotic pressure,

C = concentration of solution in moles/litre

R = gas constant = 0.082 L atm mol^{-1}K^{-1}or 8.314 J mol^{-1}K^{-1}T = absolute temperature

n = number of moles of solute,

V = volume of the solution.

Concept: Abnormal Molar Masses

Is there an error in this question or solution?