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Van der waal's constants

  • #1

Homework Statement


My book says that the constants a and b are characteristic properties of a gas, and they do not depend on temperature. But i am having trouble understanding it.

Homework Equations




The Attempt at a Solution


We know, a = ΔP*V2 / n2 , but volume is temperature dependent, so how can a be temperature independent? One explanation can be that as V increases then ΔP will decrease, so that the ratio remains constant, but i am not sure.
Similarly as I increase the temperature, volume will increase, hence b decreases, as the gas approaches ideality. Please help me out.
 

Answers and Replies

  • #2
BvU
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Hello,

but volume is temperature dependent
indeed it is. But that is a 'different volume'.

the ##b## in the van der Waals equation of state refers to the 'actual' volume of the molecules themselves. In other words: the equivalent volume of the molecules if they are considered as hard spheres. The volume the gas assumes under a given pressure and at a given temperature is much greater: most of that is simply empty space trough which the molecules move at considerable speeds. ##b## follows when you go to zero Kelvin and classically the molecules don't move any more.

##a## is a first correction on the pressure: in the ideal gas law there are no intermolecular forces and ##pV = nRT##. In a real gas there is a small, almost always attractive, force between the molecules that reduces the pressure.
 
  • #3
Okay, i understood the case of b.
But i need some clarifications regarding a.
If temperature increases, won't the intermolecular force and hence 'a' decrease ?
 
Last edited:
  • #4
BvU
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The forces decrease because the intramolecular distances increase. The effect on the pressure in lowest order is best approximated with ##a\displaystyle \left ( n\over V \right )^2 \ .##

Google intramolecular forces, van der Waals force, Lennard Jones potential
 
  • #5
Borek
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As long as all electrons are in their ground state "volume" of the molecules and strength of intermolecular forces can be assumed constant (that's not entirely true, but it is quite a good approximation). In temperatures where the VdV equation is used electrons don't get excited.
 
  • #6
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Homework Statement


My book says that the constants a and b are characteristic properties of a gas, and they do not depend on temperature. But i am having trouble understanding it.

Homework Equations




The Attempt at a Solution


We know, a = ΔP*V2 / n2 , but volume is temperature dependent, so how can a be temperature independent? One explanation can be that as V increases then ΔP will decrease, so that the ratio remains constant, but i am not sure.
By your mathematical rationale, in the ideal gas equation PV=nRT, the ideal gas constant R should be a function of the pressure, the volume, the number of moles, and the temperature. Is that correct?
 

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