Behaviour of Real Gases — Revision Notes

⚡ 30-Second Revision

Ideal Gas: — Point masses, no intermolecular forces, $PV=nRT$.
Real Gas: — Finite molecular volume, intermolecular forces present.
Deviation: — Max at low T, high P. Min (approaches ideal) at high T, low P.
Compressibility Factor (Z): — $Z = \frac{PV}{nRT}$

* $Z=1$: Ideal gas. * $Z<1$: Attractive forces dominant (gas more compressible). * $Z>1$: Molecular volume dominant (gas less compressible).

Van der Waals Equation: — $(P + \frac{an^2}{V^2})(V - nb) = nRT$

* 'a': Accounts for attractive forces (higher 'a' = stronger attraction). * 'b': Accounts for molecular volume (higher 'b' = larger molecules).

Critical Constants:

* $T_c = \frac{8a}{27Rb}$ (Critical Temperature) * $P_c = \frac{a}{27b^2}$ (Critical Pressure) * $V_c = 3b$ (Critical Volume for 1 mole)

Liquefaction: — Possible only below $T_c$.

2-Minute Revision

Real gases differ from ideal gases because their molecules have finite volume and experience intermolecular forces. These deviations are most significant at low temperatures and high pressures, where molecules are close and slow-moving.

The compressibility factor, $Z = PV/nRT$, quantifies this deviation. For ideal gases, $Z=1$. If $Z<1$, attractive forces dominate, making the gas more compressible. If $Z>1$, the finite molecular volume dominates, making the gas less compressible.

The van der Waals equation, $(P + an^2/V^2)(V - nb) = nRT$, corrects the ideal gas law. Constant 'a' accounts for attractive forces, and 'b' for molecular volume. Critical temperature ($T_c$) is the maximum temperature for liquefaction, related to 'a' and 'b' by $T_c = 8a/(27Rb)$.

Similarly, $P_c = a/(27b^2)$ and $V_c = 3b$. Remember, H2 and He often show $Z>1$ due to their negligible attractive forces.

5-Minute Revision

Let's quickly review the behavior of real gases, a crucial topic for NEET. Unlike the theoretical ideal gas, real gases have molecules with finite volume and experience intermolecular forces. These two factors cause real gases to deviate from the ideal gas law, $PV=nRT$.

The deviation is most pronounced at low temperatures (where attractive forces become significant as kinetic energy is low) and high pressures (where molecules are forced close, making their finite volume and interactions prominent).

Conversely, real gases approach ideal behavior at high temperatures and low pressures.

The compressibility factor (Z), defined as $Z = PV/nRT$, is our primary tool to quantify this deviation. For an ideal gas, $Z=1$. If $Z<1$, it indicates that attractive intermolecular forces are dominant, making the gas more compressible than ideal.

This typically occurs at moderate pressures and lower temperatures. If $Z>1$, it means the finite volume of the gas molecules is the dominant factor, making the gas less compressible. This is observed at very high pressures.

Notably, hydrogen and helium often show $Z>1$ even at moderate pressures because their attractive forces are extremely weak, and the volume effect dominates.

To better describe real gas behavior, the van der Waals equation was proposed: $(P + \frac{an^2}{V^2})(V - nb) = nRT$. Here, 'a' is the constant that corrects for attractive intermolecular forces; a larger 'a' means stronger attractions. 'b' is the constant that corrects for the finite volume of the gas molecules; a larger 'b' means larger molecules. These constants are unique for each gas.

Finally, understanding critical phenomena is vital. The **critical temperature ($T_c$) is the maximum temperature above which a gas cannot be liquefied, no matter how much pressure is applied. The critical pressure ($P_c$)** is the minimum pressure required to liquefy a gas at $T_c$.

The **critical volume ($V_c$)** is the volume occupied by one mole of gas at $T_c$ and $P_c$.

Remember to practice numerical problems involving these formulas and conceptual questions on the interpretation of Z and the significance of 'a' and 'b'.

Prelims Revision Notes

Behaviour of Real Gases: NEET Revision Notes

1. Ideal Gas vs. Real Gas:

Ideal Gas: — Hypothetical. Molecules are point masses (negligible volume). No intermolecular forces. Collisions are perfectly elastic. Obeys $PV=nRT$ strictly.
Real Gas: — Actual gases. Molecules have finite volume. Intermolecular forces (attractive and repulsive) exist. Deviates from ideal behavior.

2. Reasons for Deviation:

Finite Molecular Volume: — At high pressures, the volume occupied by molecules themselves is significant, reducing the free volume available for movement. Ideal gas law *overestimates* volume.
Intermolecular Forces: — At low temperatures and moderate pressures, attractive forces pull molecules together, reducing the frequency and force of collisions with walls. Ideal gas law *overestimates* pressure.

3. Conditions for Ideal Behavior:

High Temperature: — High kinetic energy overcomes attractive forces.
Low Pressure: — Molecules are far apart, so molecular volume and forces are negligible.

4. Conditions for Maximum Deviation:

Low Temperature: — Attractive forces are dominant.
High Pressure: — Molecular volume becomes significant, and molecules are close enough for strong interactions.

5. Compressibility Factor (Z):

Definition: $Z = \frac{PV_{real}}{nRT}$
For Ideal Gas: — $Z=1$.
For Real Gas:

* **$Z < 1$: Attractive forces dominate. Gas is more compressible than ideal. Occurs at moderate pressures, low temperatures. * $Z > 1$**: Molecular volume dominates. Gas is less compressible than ideal. Occurs at very high pressures. * **Hydrogen ($H_2$) and Helium ($He$):** Generally show $Z > 1$ at all practical pressures at room temperature due to very weak attractive forces and small size, making volume effect dominant.

6. Van der Waals Equation:

Equation: $\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$
Pressure Correction ($\frac{an^2}{V^2}$): — Added to observed pressure to account for attractive intermolecular forces. 'a' is the van der Waals constant for attractive forces. Higher 'a' means stronger attractions.
Volume Correction ($nb$): — Subtracted from observed volume to account for the finite volume of molecules. 'b' is the van der Waals constant for molecular volume (excluded volume). Higher 'b' means larger molecules.
Units: — 'a' in $ext{L}^2 \text{atm mol}^{-2}$ or $ext{m}^6 \text{Pa mol}^{-2}$. 'b' in $ext{L mol}^{-1}$ or $ext{m}^3 \text{mol}^{-1}$.

7. Critical Phenomena and Liquefaction:

Critical Temperature ($T_c$): — Maximum temperature above which a gas cannot be liquefied, regardless of pressure.
Critical Pressure ($P_c$): — Minimum pressure required to liquefy a gas at its $T_c$.
Critical Volume ($V_c$): — Volume occupied by one mole of gas at $T_c$ and $P_c$.
Relationships with van der Waals constants:

* $T_c = \frac{8a}{27Rb}$ * $P_c = \frac{a}{27b^2}$ * $V_c = 3b$ (for one mole)

Liquefaction: — Easier for gases with higher $T_c$ (stronger 'a' and smaller 'b').

Vyyuha Quick Recall

Real Gases Deviate Lots Here: Low Temp, High Pressure.

Zero Attraction, Volume Excluded: Z (Compressibility Factor) tells us if Attractions ($Z<1$) or Volume ($Z>1$) are Effective.

Van Waals' Attraction Blocks Volume: 'a' for Attraction, 'b' for Blocked Volume.