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Derive Van’T Hoff General Solution Equation - Chemistry

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Answer in Brief
Derivation

Derive van’t Hoff general solution equation 

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

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Solution

  1. 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.
  2. 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
  3. Combining (1) and (2) we get,
    π ∝ `"T"/"V"`
    ∴ π = Constant x `"T"/"V"`
    ∴ πV = R'T, where R' is a constant.
  4. 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 )
  5. This equation was derived for 1 mole of solute dissolved in V dm3. If n moles of solute are dissolved in V dmof solution, the equation becomes
    πV = nRT
    ∴ π = ` "nRT"/"V"`
  6.  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
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