Critical constant of A gas
When pressure is incerases at constant temp volume of gas decreases
AB → gases, BC → vapour + liquid, CD → liquid
critical point : At this point all the physical properties of liquid phase will be same as the physical properties in vapour such as, density of liquid = density of vapour
T C or critical temp : Temperature above which a gas can not be liquified
P C or critical pressure : minimum pressure which must be applied at critical temp to convert the gas into liquid.
V C or critical volume : volume occupied by one mole of gas at T C & P C
CRITICAL CONSTANT USING VANDER WAAL EQUATIONS :
(V m – b) = RT ⇒ ( 
) (V m – b) = RT V m 2
PV m 3 + aV m – PbV m 2 – ab – RTV m 2 = 0 ⇒ V m 3 + V m 2 
+ 
– 
= 0
Since equation is cubic in V m hence there will be three roots of equation at any temperature and pressure.
At critical point all three roots will coincide and will give single value of V m = V c
at critical point, Vander Waal equation will be
V m 3 – V m 2 
+ 
V m – 
= 0 ...
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) At critical point,
= 0 ⇒ – 
+ 
– 
= 0 ⇒ – RT C + 
– 
= 0 ⇒ RT C V 2 m – 2BV m + 3C = 0
as equation will have repeated root then D = 0 ⇒ T C = 
(ii) P C , V C and T C are given hence ‘a’ and ‘b’ should be calculated using P C and T C as it is more reliable.
P C = 
, T C = 
= 
⇒ b = 
= 
(iii) 4 × 
π r 3 . N A = 
⇒ r = 
At 100 K and pressure below 20 atm it may have liquid or gaseous state depending on the pressure
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