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Liquefaction of Gases and Critical Constants

Which of the ...

Question

Which of the following statement(s) is/are true:
I - Slope of isotherm at critical point is maximum.
II - Larger the value of $T_{c}$ , easier is the liquefaction of gas.
III - van der Waals' equation of state is applicable below critical temperature at all pressures.

Only I

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I & II

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II & III

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Only II

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Solution

The correct option is B I & II
I - Slope of isotherm below critical point $< 0$ .
Slope of isotherm above critical point $< 0$ .
but slope of isotherm at critical point $= 0$ .
So slope of isotherm at critical point is maximum.
II. As $T_{c} = \frac{8 a}{27 R b}$ $\Rightarrow T_{c} \propto (a / b)$
Larger value of $T_{c}$ means less decrease in temperature is required to liquefy the gas. So, easier will be the liquefaction.
III. When a gas is below the critical temperature, it is a 'liquid' so van der Waals equation of state in not valid.
Hence, the correct answer is option (b).

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Similar questions

Q. Which of the following statements(s) is true?
I - The slope of isotherm at the critical point is maximum.
II - Larger the value of

T_{c}

, easier is the liquification of the gas.
III - Van der Waals equation of state is applicable below critical temperature at all pressures.

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

I :

Larger the

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

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

I : Larger the $\frac{T_{c}}{P_{c}}$ value of a gas, larger would be the excluded volume.

II : Critical temperature ( $T_{c}$ ) of a gas is greater than its Boyle's temperature ( $T_{B}$ ).

III : At the critical point in the Van der Walls gas isotherm.

$⟮ \frac{d P}{d V_{m}} ⟯ T_{c} = 0$

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^{'}

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}

(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}

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Liquefaction of Gases and Critical Constants

Standard XIII Chemistry

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Which of the following statement(s) is/are true: I - Slope of isotherm at critical point is maximum. II - Larger the value of Tc, easier is the liquefaction of gas. III - van der Waals' equation of state is applicable below critical temperature at all pressures.

Which of the following statement(s) is/are true:
I - Slope of isotherm at critical point is maximum.
II - Larger the value of $T_{c}$ , easier is the liquefaction of gas.
III - van der Waals' equation of state is applicable below critical temperature at all pressures.