The equation of state for a certain gas is P = RT/(V m − b) − a/V m , where a and b are constants distinct from zero. Ascertain whether the gas has a critical point or not. Answer as 1 if the gas has

Question

The equation of state for a certain gas is P = RT/(V m − b) − a/V m , where a and b are constants distinct from zero. Ascertain whether the gas has a critical point or not. Answer as 1 if the gas has critical point and as 2, if no critical point.

TestHub · Accepted Answer

A critical point needs (dP/dV) T = 0 and (d 2 P/dV 2 ) T = 0 simultaneously. dP/dV = -RT/(V - b) 2 + a/V 2 = 0 ⇒ RT = a(V - b) 2 /V 2 . d 2 P/dV 2 = 2RT/(V - b) 3 - 2a/V 3 = 0 ⇒ RT = a(V - b) 3 /V 3 . Equating: (V - b) 3 /V 3 = (V - b) 2 /V 2 ⇒ (V - b)/V = 1 ⇒ b = 0, contradicting b =/= 0. Hence no critical point exists. Answer = 2.

Chemistry - Real Gas Question with Solution | TestHub

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