# Derive Van’T Hoff General Solution Equation - Chemistry

Derivation

Derive van’t Hoff general solution equation

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

#### 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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2014-2015 (March)

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