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van der Waals equation and its constants
JEE Advanced level
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Difficulty 3 of 3
rg180
Four moles of chlorine (
a
=
6.49
L
2
atm
mo
l
−
2
,
b
=
0.0562
L
mo
l
−
1
) are stored in a
3.00
L
cylinder at
400
K
(
R
=
0.0821
L
atm
K
−
1
mo
l
−
1
). Which statements are correct?
A
The free volume
V
−
nb
is
2.775
L
B
The pressure correction
a
n
2
/
V
2
is about
11.5
atm
C
The van der Waals pressure is about
35.8
atm
D
The compressibility factor is greater than 1
Answer: A, B, C
nb
=
4
×
0.0562
=
0.2248
L
, so
V
−
nb
=
2.775
L
(A true).
a
n
2
/
V
2
=
6.49
×
16/9.00
=
11.54
atm
(B true).
P
=
2.775
4
×
32.84
−
11.54
=
47.34
−
11.54
=
35.8
atm
(C true). Ideal pressure
=
131.36/3.00
=
43.79
atm
, so
Z
=
35.8/43.79
=
0.82
, below 1 (D false).
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