Liquefaction of gases is a process of transforming gas into its liquid form. Herein, a gas is cooled and/or its pressure is increased to an extent that it condenses into a liquid state. It is one of the basic concepts in thermodynamics, and it has innumerable practical applications in everyday life. For example, liquefied natural gas, or LNG, is used as fuel for heating and cooking. Liquefied natural gas is used to store and transport natural gas due to its minimal volume use compared to gas. Liquefied oxygen and nitrogen are other important gases in this form in the medical and industrial fields. Oxygen is required for many medical procedures and thus is stored in a liquid state in hospitals to reduce the volume of space consumed and guarantee its continuous availability. Nitrogen is also applied in food processing, where it can fast-freeze foods to preserve them. Other applications for the principles of liquefaction of gases are in air conditioning and refrigeration to make our homes and offices comfortable. In a nutshell, the liquefaction of gases makes possible and efficient storage, transportation, and application of gases in various practical applications which bring convenience and comfort in daily living.
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Critical Temperature Tc
Critical temperature of a gas may be defined as that temperature above which the gas cannot be liquefied however high the pressure is applied on the gas.
The critical temperature of a real gas is given by $\mathrm{T}_{\mathrm{c}}=\frac{8 \mathrm{a}}{27 \mathrm{Rb}}$
Critical Pressure Pc
The minimum pressure that must be applied on a gas at its critical temperature to just liquefy it.
The critical pressure of a real gas is given by $P_c=\frac{a}{27 b^2}$
Critical Volume Vc
The volume occupied by one mole of a gas at its critical temperature and critical pressure is known as the critical volume.
The critical volume of a real gas is given by $V_c=3 b$
At critical point,$\mathrm{Z}=\frac{\mathrm{P}_{\mathrm{c}} \mathrm{V}_{\mathrm{c}}}{\mathrm{RT}_{\mathrm{c}}}=\frac{3}{8}$
Significance of a and b
$
\begin{aligned}
& \text { Values of 'a' } \\
& \mathrm{He}<\mathrm{H}_2<\mathrm{O}_2<\mathrm{N}_2<\mathrm{CO}_2<\mathrm{HCl}<\mathrm{NH}_3<\mathrm{SO}_2 \\
& \mathrm{a} \rightarrow(0.034)(0.244)(1.36)(1.39)(3.59)(3.8)(4.17)(6.71)
\end{aligned}
$
Increasing order of liquefication of some gases
For a better understanding of the topic and to learn more about the Liquefaction of Gases with video lesson we provide the link to the
YouTube video:
Example 1: For a real gas the P-V curve was experimentally plotted and it had the following appearance. With respect to liquefaction. Choose the correct statement.
1)at T = 500 K, P = 40 atm, the state will be liquid.
2)at T = 300 K, P = 50 atm, the state will be gas.
3)at T < 300 K, P > 20 atm, the state will be gas.
4) at 300 K < T < 500 K, P > 50 atm, the state will be liquid.
Solution
Liquefaction of gases -
At high pressure, molecules of gas come close to each other. As a result, intermolecular attraction forces increase. When it is allowed to escape through a nozzle into a region of low pressure, the molecules move apart.
In doing so, energy is needed to overcome intermolecular attraction forces. This energy is taken from the molecules themselves. Therefore the gas is cooled.
This process is repeated many times until the gas is completely changed into the liquid state.
(a) at T = 500 K, P = 40 atm corresponds to 'a' substance - gas
(b) at T = 300 K, P = 50 atm corresponds to 'b' substance - liquid
(c) at T < 300 K, P > 20 atm corresponds to 'c' substance - liquid
(d) at T < 500 K, P > 50 atm corresponds to 'd' substance - liquid
Example 2: Critical temperatures of ammonia and carbon dioxide are 405.5 K and 304.10 K, respectively. Which of these gases will liquify first when you start cooling from 500 K to their critical temperature?
1) Ammonia
2)Carbon dioxide
3)Both will liquify at same time
4)Nothing can be predicted
Solution
Since the critical temperature of ammonia is higher than that of carbon dioxide, ammonia will liquify first as its critical temperature will be reached first. The liquefaction of carbon dioxide will require cooling to a lower temperature.
Hence, the answer is the option (1).
Example 3: Critical temperature for carbon dioxide and methane are $31.1^{\circ}$ and $-81.9^{\circ} \mathrm{C}$ respectively. Which of these has stronger intermolecular forces?
1) Carbon dioxide
2)Methane
3)Both have same intermolecular forces
4)Nothing can be predicted
Solution
We have1:
$T_c$ for $\mathrm{CH}_4=-81.9^{\circ} \mathrm{C}$ and $T_c$ for $\mathrm{CO}_2=31.1^{\circ} \mathrm{C}$
Clearly, $\mathrm{CO}_2$ has more vital intermolecular forces of attraction as it has a higher value of critical temperature.
Hence, the answer is the option (1).
Example 4: The critical temperature of $\mathrm{O}_2$ is less than $\mathrm{H}_2 \mathrm{O}$ because the $\mathrm{H}_2 \mathrm{O}$ molecules have:
1)Two covalent bonds
2) Dipole moment
3)Fewer electrons than $\mathrm{O}_2$
4)V-shaped structure
Solution
We know that the dipole moment in a molecule results in strong intermolecular forces and since
$T_c=\frac{8 a}{27 R b}$
Thus, the critical temperature of $\mathrm{H}_2 \mathrm{O}$ is more for $\mathrm{O}_2$ .
Hence, the answer is the option (2).
Liquefaction of gases is the process whereby gases are converted to liquids either by cooling and/or under increased pressure. This is very important in storage and transportation because it takes less space than the gas. For example, natural gas is liquefied primarily, hence the term LNG, for storage and transportation, especially to homes for heating and cooking. Liquid oxygen becomes an important element in medical operations, so it is stored as a liquid to supply patients continuously. Liquid nitrogen is used industrially for fast freezing during food processing to ensure it remains wholesome and safe for consumption. The concepts of gas liquefaction are also applied in air conditioning and refrigeration to cool our surrounding environments for a better life with more comfort. Everything would generally make a vast difference in the application of the liquefaction of gases in diverse industries, especially in contributing mainly to health, food preservation, the convenience of delivery, and efficiency in human life.
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