Gas Laws ✏ Chemistry In a Nutshell

Rucete ✏ Chemistry In a Nutshell

1. Fundamental Gas Laws

These laws describe the relationships between pressure (P), volume (V), temperature (T), and the number of moles (n) in gases.

Gas Law	Statement	Equation
Avogadro's Law	At constant temperature and pressure, volume is proportional to the number of moles.	$V\propto n$ or $\frac{V_1}{n_1}=\frac{V_2}{n_2}$
Boyle's Law	At constant temperature, pressure and volume are inversely proportional.	$P_1{V}_1=P_2{V}_2$
Charles' Law	At constant pressure, volume and temperature are directly proportional.	$\frac{V_1}{T_1}=\frac{V_2}{T_2}$
Gay-Lussac's Law	At constant volume, pressure and temperature are directly proportional.	$\frac{P_1}{T_1}=\frac{P_2}{T_2}$
Combined Gas Law	Combines Boyle's, Charles', and Gay-Lussac's laws into one equation.	$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

2. Dalton’s Law of Partial Pressures

• Total pressure of a gas mixture equals the sum of the individual gas pressures.
• Equation:$$P_{\text{total}}=P_1+P_2+P_3+\dots$$
  
• Partial pressure of a gas is determined by its mole fraction:$$P_A={\chi }_A\cdot P_{\text{total}}$$
  
  • ${\chi }_A=\frac{n_A}{n_{\text{total}}}$ (mole fraction of gas A)

3. Graham’s Law of Diffusion & Effusion

• Diffusion: Gradual mixing of gases.
• Effusion: Gas particles passing through a tiny hole without collisions.
• Rate of diffusion or effusion is inversely proportional to the square root of molar mass.
• Equation:$$\frac{{\text{Rate}}_1}{{\text{Rate}}_2}=\sqrt{\frac{M_2}{M_1}}$$
  • Lighter gases diffuse faster than heavier gases.

4. Ideal Gas Law

• Describes the behavior of an ideal gas.

• Equation:

  $$PV=nRT$$
  
  • $\mathrm{<br>}$ = Pressure (atm)
  • $V$ = Volume (L)
  • $n$ = Moles of gas
  • $R$ = Gas constant (0.0821 L·atm/mol·K)
  • $T$ = Temperature (K)

• Real gases behave ideally at high temperature and low pressure.

5. Van der Waals Equation (Real Gas Behavior)

• Corrects for intermolecular forces and gas particle volume.
• Equation:$$(P+\frac{a}{V^2})(V-b)=nRT$$
  
  • "a" corrects for intermolecular forces.
  • "b" corrects for gas particle volume.
  • Deviations occur at low temperature and high pressure.

6. Gas Density

• Density of a gas ($d$) can be calculated using:$$d=\frac{PM}{RT}$$
  
  • $M$ = Molar mass
  • $P$ = Pressure
  • $R$ = Gas constant
  • $T$ = Temperature

In a nutshell

• Boyle’s Law: Pressure increases, volume decreases.
• Charles’ Law: Temperature increases, volume increases.
• Avogadro’s Law: More moles = More volume.