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Standard VIII

Chemistry

Gases

If Pc, Vc and...

Question

If Pc, Vc and Tc are critical pressure, critical volume and critical temperature, then compressibility factor at critical condition is (1) 0.375(3) 1.275(2) 2.66(4) 1

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Q. The vander waal's equation of corresponding states for 1 mole of gas is [where

P_{c} =

critical pressure,

T_{c} =

critical temperature,

V_{c} =

critical volume]

[π = \frac{P}{P_{c}}, ϕ = \frac{V}{V_{c}} a n d θ = \frac{T}{T_{c}}]

Q. Assertion :The numerical values of

P_{c}, V_{c}, T_{c}

are

\frac{a}{27 b^{2}}, 3 b

and

\frac{8 a}{27 R b}

respectively. Reason: The compressibility factor

Z

at critical conditions is

\frac{3}{8}

Q. If

\frac{P}{P_{c}} = P_{r}, \frac{T}{T_{c}} = T_{r}, a n d \frac{V_{m}}{V_{m, c}} = V_{r}

where

P_{r}

is reduced pressure,

P_{c}

is critical pressure

T_{r}

is reduced temperature,

T_{c}

is critical temperature

V_{r}

is reduced volume,

V_{c}

is critical volume
then the equation of state (or van der Waals equation), only in terms of

P_{r}, T_{r}

and

V_{r}

The essential conditions for liquefaction of gases were discovered by Andrews in

1869

as a result of his study of pressure-volume-temperature relationship for

C O_{2}

. It was found that above a certain temperature, it was impossible to liquefy a gas whatever the pressure was applied. The temperature below which the gas can be liquefied by the application of pressure alone is called critical temperature

(T_{c})

. The pressure required to liquefy a gas at this temperature is called the critical pressure

(P_{c)}

. The volume occupied by one mole of the substance at the critical temperature and pressure is called critical volume. Critical constants are related with van der Waals' constant as follows:

V_{c} = 3 b, P_{c} = \frac{a}{27 b^{2}}, T_{c} = \frac{8 a}{27 R b}

The relationship between

P_{C}, V_{C}

and

T_{C}

The critical temperature $(T_{c})$ and critical pressure $p_{c})$ of $C O_{2}$ are ${30.98}^{\circ} C$ and 73 atm respectively.Can $C O_{2}$ (g) be liquefied at $32^{\circ} C$ and 80 atm pressure?

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