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Questions
Derive van’t Hoff general solution equation
Derive van’t Hoff general solution equation for ‘n’ moles of solute.
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 dm3. If n moles of solute are dissolved in V dm3 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.
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