Liquefaction of Gases — Revision Notes

⚡ 30-Second Revision

Liquefaction: — Gas to liquid.
Conditions: — Low temperature, high pressure.
Critical Temperature ($T_c$): — Max temp for liquefaction. Above $T_c$, no liquefaction.
Critical Pressure ($P_c$): — Min pressure at $T_c$ for liquefaction.
Ease of Liquefaction: — $\propto T_c \propto$ strength of intermolecular forces (van der Waals 'a').
Joule-Thomson Effect: — Cooling on adiabatic expansion for most gases.
Inversion Temperature ($T_i$): — Gas cools if $T < T_i$; heats if $T > T_i$.
$\text{H}_2, \text{He}$: — Low $T_i$, need pre-cooling for J-T cooling.
Andrews' Isotherms: — P-V curves showing gas, liquid, and coexistence regions below $T_c$.

2-Minute Revision

Liquefaction of gases is the process of converting a gas into a liquid, achieved by lowering its temperature and/or increasing its pressure. The most critical concept is the **critical temperature ($T_c$)**, which is the maximum temperature above which a gas cannot be liquefied, regardless of the pressure applied.

Below $T_c$, a gas can be liquefied by applying sufficient pressure, known as the **critical pressure ($P_c$)**. Gases with stronger intermolecular forces have higher $T_c$ values and are thus easier to liquefy.

The Joule-Thomson effect is a key principle in industrial liquefaction, where most gases cool upon adiabatic expansion from high to low pressure. This cooling occurs because molecules do work against their attractive forces.

However, this effect only leads to cooling if the gas is below its **inversion temperature ($T_i$)**. Gases like hydrogen and helium have very low $T_i$ and must be pre-cooled before they can be cooled by the Joule-Thomson effect.

Andrews' experiments on $ext{CO}_2$ graphically demonstrated these critical phenomena through P-V isotherms.

5-Minute Revision

To master liquefaction of gases, start with the fundamental idea: converting gas to liquid by making intermolecular attractive forces dominant over molecular kinetic energy. This is achieved by decreasing temperature (reducing kinetic energy) and/or increasing pressure (forcing molecules closer).

The absolute limit for this process is the **critical temperature ($T_c$)**. Above $T_c$, a gas cannot be liquefied, period. Below $T_c$, a specific minimum pressure, the **critical pressure ($P_c$)**, is required.

Gases with stronger intermolecular forces (e.g., $ext{NH}_3$ due to hydrogen bonding) have higher $T_c$ values and are therefore easier to liquefy. Conversely, gases with weak forces (e.g., $ext{He}$) have very low $T_c$ and are extremely difficult to liquefy.

Andrews' experiments on $ext{CO}_2$ provided the empirical evidence. His P-V isotherms showed that below $T_c$, there's a distinct horizontal plateau where gas and liquid coexist at constant pressure (vapor pressure). At $T_c$, this plateau shrinks to a single point, the critical point, where liquid and gas become indistinguishable.

For practical liquefaction, the Joule-Thomson effect is crucial. When a real gas expands adiabatically through a porous plug, it generally cools down. This cooling happens because the gas molecules expend their internal energy to overcome the attractive forces between them as they move apart.

However, this cooling effect is only observed if the gas's temperature is below its **inversion temperature ($T_i$)**. If the temperature is above $T_i$, the gas will actually heat up upon expansion. This is why gases like hydrogen and helium, with their very low $T_i$, must be pre-cooled significantly before the Joule-Thomson effect can be used to liquefy them.

Remember, the van der Waals constants 'a' (intermolecular forces) and 'b' (molecular volume) are directly linked to $T_c$ and $P_c$, providing a theoretical basis for these observations.

Prelims Revision Notes

Liquefaction of Gases: NEET Quick Facts

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Definition: — Conversion of a gas into a liquid state.
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Conditions: — Low temperature (reduces kinetic energy) and high pressure (brings molecules closer).
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**Critical Temperature ($T_c$):**

* Maximum temperature above which a gas cannot be liquefied by any pressure. * Unique for each gas. * Higher $T_c$ means stronger intermolecular forces and easier liquefaction. * $T_c = \frac{8a}{27Rb}$ (where 'a' is van der Waals constant for attractive forces).

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**Critical Pressure ($P_c$):**

* Minimum pressure required to liquefy a gas at its critical temperature. * $P_c = \frac{a}{27b^2}$.

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**Critical Volume ($V_c$):**

* Volume occupied by one mole of gas at $T_c$ and $P_c$. * $V_c = 3b$.

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**Andrews' Isotherms for $\text{CO}_2$:**

* P-V curves at constant temperature. * Above $T_c$: Behaves like an ideal gas (no liquefaction). * At $T_c$: Critical point (C) where gas and liquid phases are indistinguishable. * Below $T_c$: Shows distinct regions: pure gas, gas-liquid coexistence (horizontal plateau at constant vapor pressure), pure liquid (steep curve).

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Joule-Thomson Effect:

* Temperature change upon adiabatic expansion of a real gas through a porous plug. * Most gases cool down due to work done against intermolecular attractive forces.

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**Inversion Temperature ($T_i$):**

* Temperature above which a gas heats on expansion; below which it cools. * For $\text{H}_2$ and $\text{He}$, $T_i$ is very low (e.g., $\text{H}_2 \approx 204 \text{ K}$, $\text{He} \approx 40 \text{ K}$). They must be pre-cooled below $T_i$ for J-T cooling.

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Ease of Liquefaction Order: — Directly proportional to $T_c$. Higher $T_c \implies$ easier to liquefy (e.g., $\text{NH}_3 > \text{CO}_2 > \text{O}_2 > \text{He}$).

Vyyuha Quick Recall

To remember the conditions for liquefaction and the role of critical temperature: 'Liquefy Gases Coolly, Pressure High. Too Cold, No Liquid, No Matter Pressure.'

Liquefy Gases: Liquefaction of Gases
Coolly, Pressure High: Low Temperature, High Pressure are conditions.
Too Cold: Refers to Critical Temperature ($T_c$)
No Liquid, No Matter Pressure: Above $T_c$, no liquefaction possible, regardless of pressure.