Deviation from Ideal Gas Behaviour — Revision Notes

⚡ 30-Second Revision

Ideal Gas: — Point masses, no intermolecular forces, $PV=nRT$, $Z=1$.\n- Real Gas: Finite volume, intermolecular forces, deviates from $PV=nRT$.\n- Deviation Conditions: High P, Low T (significant deviation); Low P, High T (approaches ideal).\n- Compressibility Factor (Z): $Z = \frac{PV}{nRT}$.\n - $Z=1$: Ideal gas.\n - $Z<1$: Attractive forces dominate, more compressible.\n - $Z>1$: Repulsive forces/molecular volume dominate, less compressible.\n- van der Waals Equation: $(P + \frac{an^2}{V^2})(V - nb) = nRT$.\n - 'a' (attraction constant): Measures attractive forces. Larger 'a' $\implies$ easier liquefaction.\n - 'b' (co-volume): Measures molecular volume. Larger 'b' $\implies$ larger molecules.\n- **Boyle Temperature ($T_B$):** Temperature where $Z \approx 1$ over a range of P. $T_B = \frac{a}{Rb}$.

2-Minute Revision

Real gases deviate from ideal behavior due to two main factors: the finite volume occupied by gas molecules and the presence of intermolecular forces. These deviations are most significant at high pressures and low temperatures.

To quantify this, we use the compressibility factor, $Z = \frac{PV}{nRT}$. For an ideal gas, $Z=1$. If $Z<1$, attractive forces between molecules are dominant, making the gas more compressible than ideal.

If $Z>1$, the finite volume of molecules and repulsive forces are dominant, making the gas less compressible. Gases like $H_2$ and $He$ typically show $Z>1$ always because their attractive forces are very weak.

The van der Waals equation, $(P + \frac{an^2}{V^2})(V - nb) = nRT$, provides a more accurate model by introducing correction terms: 'a' for attractive forces (larger 'a' means easier liquefaction) and 'b' for the molecular volume (larger 'b' means larger molecules).

Real gases approach ideal behavior at high temperatures and low pressures, and specifically at the Boyle temperature ($T_B = \frac{a}{Rb}$), where Z is approximately 1 over a range of pressures.

5-Minute Revision

The ideal gas law, $PV=nRT$, is a simplification based on assumptions of negligible molecular volume and no intermolecular forces. Real gases, however, deviate from this ideal behavior because their molecules do occupy a finite volume and exert attractive and repulsive forces on each other.

These deviations become prominent under conditions of high pressure (molecules are close, so their volume and repulsive forces matter) and low temperature (molecules move slower, allowing attractive forces to dominate).

\n\nTo measure this deviation, we use the compressibility factor, $Z = \frac{PV}{nRT}$. For an ideal gas, $Z=1$. \n* When $Z<1$, the real gas is more compressible than an ideal gas. This occurs when attractive intermolecular forces are dominant, pulling molecules closer together and reducing the actual volume.

This is typically seen at moderate pressures and lower temperatures. \n* When $Z>1$, the real gas is less compressible than an ideal gas. This happens when the finite volume of the molecules themselves becomes significant, leading to effective repulsive forces.

This is observed at very high pressures, or for gases with very weak attractive forces like $H_2$ and $He$, where $Z$ is always greater than 1. \n\nThe van der Waals equation, $(P + \frac{an^2}{V^2})(V - nb) = nRT$, is a crucial improvement.

It introduces two constants: \n1. 'a' (pressure correction): Accounts for attractive intermolecular forces. A larger 'a' value indicates stronger attractive forces, making the gas easier to liquefy.

\n2. 'b' (volume correction): Accounts for the finite volume of the gas molecules (excluded volume). A larger 'b' value indicates larger molecular size. \n\nReal gases behave most ideally at high temperatures and low pressures.

The Boyle temperature ($T_B = \frac{a}{Rb}$) is a specific temperature at which a real gas behaves ideally over a significant range of pressures, meaning $Z \approx 1$. Understanding these concepts is vital for interpreting gas behavior in various contexts.

Prelims Revision Notes

Deviation from Ideal Gas Behaviour: NEET Revision Notes\n\n1. Ideal Gas vs. Real Gas:\n * Ideal Gas: Hypothetical. Negligible molecular volume. No intermolecular forces. Obeys $PV=nRT$. $Z=1$ always.\n * Real Gas: Actual. Finite molecular volume. Intermolecular forces (attractive & repulsive). Deviates from $PV=nRT$.\n\n2. Conditions for Deviation/Ideal Behavior:\n * Maximum Deviation: High Pressure, Low Temperature (molecules close, slow-moving $\implies$ forces & volume significant).\n * Approaches Ideal Behavior: Low Pressure, High Temperature (molecules far apart, fast-moving $\implies$ forces & volume negligible).\n\n3. Compressibility Factor (Z):\n * Definition: $Z = \frac{PV}{nRT}$. It quantifies deviation.\n * $Z=1$: Ideal gas behavior.\n * $Z<1$: Attractive forces dominate. $V_\text{real} < V_\text{ideal}$. Gas is more compressible than ideal. Occurs at moderate P, low T.\n * $Z>1$: Repulsive forces / finite molecular volume dominate. $V_\text{real} > V_\text{ideal}$. Gas is less compressible than ideal. Occurs at very high P, or for $H_2/He$ even at moderate P.\n * Z vs. P Graphs:\n * Ideal gas: Horizontal line at $Z=1$.\n * Most gases ($N_2, O_2, CO_2$): Dip below $Z=1$ (attractive forces) then rise above $Z=1$ (molecular volume/repulsive forces).\n * $H_2, He$: Always $Z>1$ and increases with P (very weak attractive forces, molecular volume dominates early).\n\n4. van der Waals Equation:\n * Equation: $(P + \frac{an^2}{V^2})(V - nb) = nRT$\n * Constant 'a' (Pressure Correction):\n * Accounts for attractive intermolecular forces.\n * Larger 'a' $\implies$ stronger attractive forces $\implies$ easier liquefaction.\n * Units: $\text{L}^2 \text{ atm mol}^{-2}$ or $\text{Pa m}^6 \text{ mol}^{-2}$.\n * Constant 'b' (Volume Correction):\n * Accounts for finite volume of gas molecules (excluded volume).\n * Larger 'b' $\implies$ larger molecular size.\n * Units: $\text{L mol}^{-1}$ or $\text{m}^3 \text{ mol}^{-1}$.\n\n5. Boyle Temperature ($T_B$):\n * Temperature at which a real gas behaves ideally over a significant pressure range ($Z \approx 1$).\n * At $T_B$, attractive and repulsive forces effectively cancel out.\n * $T_B = \frac{a}{Rb}$.\n\n6. Critical Constants ($T_c, P_c, V_c$):\n * Critical Temperature ($T_c$): Max temperature above which a gas cannot be liquefied, regardless of pressure. $T_c = \frac{8a}{27Rb}$.\n * Critical Pressure ($P_c$): Minimum pressure required to liquefy a gas at its critical temperature. $P_c = \frac{a}{27b^2}$.\n * Critical Volume ($V_c$): Volume occupied by one mole of gas at $T_c$ and $P_c$. $V_c = 3b$.

Vyyuha Quick Recall

To remember the conditions for ideal gas behavior: High Temperature, Low Pressure. Think: 'Hot & Loose' molecules behave ideally. For Z values: Zero < 1 means Attractive forces (Z is 'A'ttracted down). Zero > 1 means Repulsive forces (Z is 'R'epelled up).