States of Matter: Gases and Liquids — Revision Notes

⚡ 30-Second Revision

Ideal Gas Equation: — $PV = nRT$
Combined Gas Law: — $rac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ (T in Kelvin)
Dalton's Law: — $P_{\text{total}} = sum P_i$, $P_i = chi_i P_{\text{total}}$
Graham's Law: — $rac{\text{Rate}_1}{\text{Rate}_2} = sqrt{\frac{M_2}{M_1}}$
Molecular Speeds: — $u_{\text{rms}} = sqrt{\frac{3RT}{M}}$, $u_{\text{avg}} = sqrt{\frac{8RT}{pi M}}$, $u_{\text{mp}} = sqrt{\frac{2RT}{M}}$
Compressibility Factor: — $Z = \frac{PV}{nRT}$ ($Z=1$ for ideal gas)
van der Waals Equation: — left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT
IMFs: — Dispersion < Dipole-Dipole < Hydrogen Bonding
Liquid Properties: — Higher IMFs $implies$ Lower VP, Higher BP, Higher Surface Tension, Higher Viscosity

2-Minute Revision

Gases are characterized by widely spaced molecules with negligible IMFs, leading to indefinite shape/volume and high compressibility. Key gas laws include Boyle's ($PV=\text{const}$), Charles's ($V/T=\text{const}$), Gay-Lussac's ($P/T=\text{const}$), and Avogadro's ($V/n=\text{const}$), all combined into the Ideal Gas Equation ($PV=nRT$).

Remember to use Kelvin for temperature. Dalton's Law states total pressure is the sum of partial pressures ($P_i = chi_i P_{\text{total}}$). Graham's Law relates effusion/diffusion rates inversely to the square root of molar mass ($ext{Rate} propto 1/sqrt{M}$).

The Kinetic Molecular Theory explains gas behavior. Real gases deviate from ideal behavior due to finite molecular volume and IMFs, quantified by the compressibility factor ($Z=PV/nRT$). $Z<1$ indicates dominant attractive forces, $Z>1$ dominant repulsive forces/molecular volume.

The van der Waals equation corrects for these deviations. Liquids have closer molecules with significant IMFs, giving definite volume but indefinite shape. Their properties (vapor pressure, boiling point, surface tension, viscosity) are directly influenced by IMF strength.

Stronger IMFs lead to lower vapor pressure, higher boiling point, higher surface tension, and higher viscosity.

5-Minute Revision

Start with the fundamental differences between gases and liquids: gases have negligible intermolecular forces (IMFs) and molecular volume, leading to high compressibility and indefinite shape/volume. Liquids have significant IMFs, definite volume, but indefinite shape, and are nearly incompressible.

The Kinetic Molecular Theory (KMT) provides the foundation for gas behavior: particles are in constant random motion, collisions are elastic, and average kinetic energy is proportional to absolute temperature ($KE_{avg} propto T$).

For ideal gases, master the gas laws: Boyle's ($P_1V_1=P_2V_2$), Charles's ($rac{V_1}{T_1}=\frac{V_2}{T_2}$), Gay-Lussac's ($rac{P_1}{T_1}=\frac{P_2}{T_2}$), and Avogadro's ($rac{V_1}{n_1}=\frac{V_2}{n_2}$).

Combine these into the Ideal Gas Equation ($PV=nRT$). Always convert temperature to Kelvin. Dalton's Law of Partial Pressures ($P_{\text{total}} = sum P_i$) and the relationship $P_i = chi_i P_{\text{total}}$ are crucial for gas mixtures.

Graham's Law of Diffusion/Effusion ($rac{\text{Rate}_1}{\text{Rate}_2} = sqrt{\frac{M_2}{M_1}}$) is important for comparing gas speeds.

Real gases deviate from ideal behavior due to two factors: finite molecular volume and intermolecular attractive forces. The compressibility factor ($Z = PV/nRT$) quantifies this deviation: $Z=1$ for ideal gases.

$Z<1$ indicates attractive forces dominate (e.g., at low T, moderate P), making the gas more compressible. $Z>1$ indicates repulsive forces or molecular volume dominates (e.g., at high P), making the gas less compressible.

The van der Waals equation left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT corrects for these, where 'a' accounts for IMFs and 'b' for molecular volume.

For liquids, focus on intermolecular forces: London dispersion (weakest, in all molecules), dipole-dipole (in polar molecules), and hydrogen bonding (strongest, specific to H-N/O/F). These forces dictate liquid properties: stronger IMFs lead to lower vapor pressure (less escape tendency), higher boiling point (more energy to overcome forces), higher surface tension (stronger inward pull), and higher viscosity (greater resistance to flow).

Understand these qualitative relationships for comparative questions.

Prelims Revision Notes

Gases: Key Concepts and Formulas

1
Ideal Gas Assumptions: — Negligible molecular volume, no intermolecular forces, elastic collisions, random motion, $KE_{avg} propto T$.
2
Temperature Conversion: — Always use Kelvin: $T(\text{K}) = T(^circ\text{C}) + 273.15$.
3
Gas Laws:

* Boyle's Law: $P propto \frac{1}{V}$ (constant $T, n$) $implies P_1V_1 = P_2V_2$ * Charles's Law: $V propto T$ (constant $P, n$) $implies \frac{V_1}{T_1} = \frac{V_2}{T_2}$ * Gay-Lussac's Law: $P propto T$ (constant $V, n$) $implies \frac{P_1}{T_1} = \frac{P_2}{T_2}$ * Avogadro's Law: $V propto n$ (constant $P, T$) $implies \frac{V_1}{n_1} = \frac{V_2}{n_2}$

1
Ideal Gas Equation: — $PV = nRT$

* $R = 0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$ or $8.314,\text{J mol}^{-1}\text{K}^{-1}$ * Density: $d = \frac{PM}{RT}$ * Molar Mass: $M = \frac{dRT}{P}$

1
Dalton's Law of Partial Pressures:

* $P_{\text{total}} = P_1 + P_2 + dots$ * $P_i = chi_i P_{\text{total}}$ (where $chi_i$ is mole fraction)

1
Graham's Law of Diffusion/Effusion:

* $rac{\text{Rate}_1}{\text{Rate}_2} = sqrt{\frac{M_2}{M_1}} = sqrt{\frac{d_2}{d_1}}$

1
Kinetic Molecular Theory (KMT) Speeds:

* Average $KE = \frac{3}{2}kT = \frac{3}{2}\frac{R}{N_A}T$ * $u_{\text{rms}} = sqrt{\frac{3RT}{M}}$, $u_{\text{avg}} = sqrt{\frac{8RT}{pi M}}$, $u_{\text{mp}} = sqrt{\frac{2RT}{M}}$ * Order: $u_{\text{mp}} < u_{\text{avg}} < u_{\text{rms}}$

1
Real Gases:

* Deviate from ideal at high P, low T. * **Compressibility Factor ($Z$):** $Z = \frac{PV}{nRT}$ * $Z=1$: Ideal gas * $Z<1$: Attractive forces dominate (gas more compressible than ideal) * $Z>1$: Repulsive forces/molecular volume dominate (gas less compressible than ideal) * van der Waals Equation: left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT * 'a': accounts for attractive forces (larger 'a' = stronger forces) * 'b': accounts for molecular volume (larger 'b' = larger molecules)

Liquids: Key Concepts

1
Intermolecular Forces (IMFs):

* Dispersion Forces: Weakest, in all molecules, increases with size/surface area. * Dipole-Dipole Forces: In polar molecules. * Hydrogen Bonding: Strongest, H bonded to N, O, or F.

1
Vapor Pressure (VP): — Pressure of vapor in equilibrium with liquid.

* Increases with T. * Decreases with stronger IMFs. * Independent of surface area.

1
Boiling Point (BP): — Temperature where VP = external pressure.

* Normal BP at $1,\text{atm}$. * Increases with stronger IMFs.

1
Surface Tension ($gamma$): — Energy to increase surface area.

* Increases with stronger IMFs. * Decreases with T.

1
Viscosity ($eta$): — Resistance to flow.

* Increases with stronger IMFs, larger/complex molecules. * Decreases with T.

Vyyuha Quick Recall

For Gas Laws: "People Very Tired, Never Rest!" (PV=nRT) For IMF strength: "Lazy Dogs Hate Bones" (London < Dipole-Dipole < Hydrogen Bonding)