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Author Topic: What is the relation between van der waal constant and radius of molecule ?  (Read 636 times)

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Motutu

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I am following 8th edition of peter atkins physical chemistry.

In this book it is given that ##b = 4* \text{volume of molecule} *N_a##
But in the solution manual it is given that ##b = 8*\text{volume of molecule} *N_a##.

I am confused as to what is the real relation between these two.

Here is the question in whose solution it is given that ##b = 8*\text{volume of molecule} *N_a## :-
The critical constants of ethane are ##P_c = 48.20 atm, V_c = 148 cm^3, T_c = 305.4 K## (a) calculate the value of b. (b) calculate the the radius of the molecule.

I calculated the value of b as 0.049 dm^3mol^(-1) and radius as 1.70 * 10^(-10) m .
My answer for b is correct but not for radius, in the solution it is given as 1.35 * 10^(-10) m. ??? ??? ??? ??? ??? ??? ???
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mjc123

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I would assume the factor of 8 is correct. 8* molecular volume is the volume of a sphere of twice the molecular radius, which is (simplistically) the volume from which the centre of another molecule is excluded by the presence of the first molecule.
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Motutu

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I would assume the factor of 8 is correct. 8* molecular volume is the volume of a sphere of twice the molecular radius, which is (simplistically) the volume from which the centre of another molecule is excluded by the presence of the first molecule.

But on wikipedia it is mentioned that factor of 4 is correct. I am very confused  ??? ??? ??? ???

Look below derivation, https://en.wikipedia.org/wiki/Van_der_Waals_equation
And here is given that the factor is 1, http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/waal.html
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mjc123

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Well, it's all rather unreal, isn't it? We know that molcules aren't really hard spheres. Even those that are spherical are not like billiard balls with a clearly defined radius. My edition of Atkins (2nd) doesn't give these derivations, and simply says b is best treated as a purely empirical parameter.
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Motutu

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Then why students are taught this, this is complete bulls&$#. If this is empirical then why should we confuse the hell out of students.
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mjc123

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Scientists don't like mere "fudge factors". They like to have an explanation for things. And treating b as the excluded volume of the molecules does give a reasonable estimate of the molecular size. But I think the formulae do give a spurious feeling of exactness to what is not exact - as I said, molecules are not hard spheres.
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