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Liquefaction of Gases and Critical Constants

The essential...

Question

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

Which of the following parameters is three times the van der Waals' constant $^{'} b^{'}$ ?

A

Critical volume

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B

Critical temperature

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C

Vapour density

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D

Critical pressure

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Solution

The correct option is A Critical volume
Critical volume is three times the van der Waals' constant ′b′.

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

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Similar questions

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}

T_{C}

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

Q. Which of the following statements on critical constants of gases are correct?

I :

T_{c} / p_{c}

value of a gas, larger would be the excluded volume.

I I :

Critical temperature

(T_{c})

of a gas is greater than its Boyles's temperature

(T_{b})

.

I I I :

At the critical point in the van der Waals' gas isotherm.

(\frac{δ p}{δ V_{m}}) T_{c} = 0

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

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}

V_{r}

Consider the following statements.

I. Gaseous substances whose critical temperatures are above room temperatures can be liquefied by applying sufficient pressure to the gas.

II. Gaseous substances whose critical temperatures are below room temperature can be liquefied by the application of pressure and lowering of temperature below $T_{c}$ .

Select the correct alternate.

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